Tian, Gang 1958
Overview
Works:  18 works in 93 publications in 1 language and 1,988 library holdings 

Genres:  Conference papers and proceedings Biography 
Roles:  Author, Other, Editor 
Publication Timeline
.
Most widely held works by
Gang Tian
Symplectic geometry and mirror symmetry : proceedings of the 4th KIAS Annual International Conference, Korea Institute for
Advanced Study, Seoul, South Korea, 1418 August 2000 by
K Fukaya(
)
2 editions published in 2001 in English and held by 352 WorldCat member libraries worldwide
In 1993, M Kontsevich proposed a conceptual framework for explaining the phenomenon of mirror symmetry. Mirror symmetry had been discovered by physicists in string theory as a duality between families of threedimensional CalabiYau manifolds. Kontsevich's proposal uses Fukaya's construction of the A 8 category of Lagrangian submanifolds on the symplectic side and the derived category of coherent sheaves on the complex side. The theory of mirror symmetry was further enhanced by physicists in the language of Dbranes and also by StromingerYauZaslow in the geometric setup of (special) Lagran
2 editions published in 2001 in English and held by 352 WorldCat member libraries worldwide
In 1993, M Kontsevich proposed a conceptual framework for explaining the phenomenon of mirror symmetry. Mirror symmetry had been discovered by physicists in string theory as a duality between families of threedimensional CalabiYau manifolds. Kontsevich's proposal uses Fukaya's construction of the A 8 category of Lagrangian submanifolds on the symplectic side and the derived category of coherent sheaves on the complex side. The theory of mirror symmetry was further enhanced by physicists in the language of Dbranes and also by StromingerYauZaslow in the geometric setup of (special) Lagran
Canonical metrics in Kähler geometry by
Gang Tian(
Book
)
15 editions published between 1999 and 2000 in English and Undetermined and held by 330 WorldCat member libraries worldwide
"The aim of this monograph is to give an essentially selfcontained introduction to the theory of canonical Kahler metrics on complex manifolds. It also presents the reader with some advanced topics in complex differential geometry not easily found elsewhere. The topics include CalabiFutaki invariants, extremal Kahler metrics, the CalabiYau theorem on existence of Kahler Ricciflat metrics, and recent progress on KahlerEinstein metrics with positive scalar curvature. Applications of KahlerEinstein metrics to the uniformization theory are also discussed." "Readers with a good general knowledge of differential geometry and partial differential equations should be able to grasp and appreciate the materials in this monograph."Jacket
15 editions published between 1999 and 2000 in English and Undetermined and held by 330 WorldCat member libraries worldwide
"The aim of this monograph is to give an essentially selfcontained introduction to the theory of canonical Kahler metrics on complex manifolds. It also presents the reader with some advanced topics in complex differential geometry not easily found elsewhere. The topics include CalabiFutaki invariants, extremal Kahler metrics, the CalabiYau theorem on existence of Kahler Ricciflat metrics, and recent progress on KahlerEinstein metrics with positive scalar curvature. Applications of KahlerEinstein metrics to the uniformization theory are also discussed." "Readers with a good general knowledge of differential geometry and partial differential equations should be able to grasp and appreciate the materials in this monograph."Jacket
Ricci flow and geometric applications : Cetraro, Italy 2010 by
Michel Boileau(
)
10 editions published in 2016 in English and held by 305 WorldCat member libraries worldwide
Presenting some impressive recent achievements in differential geometry and topology, this volume focuses on results obtained using techniques based on Ricci flow. These ideas are at the core of the study of differentiable manifolds. Several very important open problems and conjectures come from this area and the techniques described herein are used to face and solve some of them. The book’s four chapters are based on lectures given by leading researchers in the field of geometric analysis and lowdimensional geometry/topology, respectively offering an introduction to: the differentiable sphere theorem (G. Besson), the geometrization of 3manifolds (M. Boileau), the singularities of 3dimensional Ricci flows (C. Sinestrari), and Kähler–Ricci flow (G. Tian). The lectures will be particularly valuable to young researchers interested in differential manifolds
10 editions published in 2016 in English and held by 305 WorldCat member libraries worldwide
Presenting some impressive recent achievements in differential geometry and topology, this volume focuses on results obtained using techniques based on Ricci flow. These ideas are at the core of the study of differentiable manifolds. Several very important open problems and conjectures come from this area and the techniques described herein are used to face and solve some of them. The book’s four chapters are based on lectures given by leading researchers in the field of geometric analysis and lowdimensional geometry/topology, respectively offering an introduction to: the differentiable sphere theorem (G. Besson), the geometrization of 3manifolds (M. Boileau), the singularities of 3dimensional Ricci flows (C. Sinestrari), and Kähler–Ricci flow (G. Tian). The lectures will be particularly valuable to young researchers interested in differential manifolds
Ricci flow and the Poincaré conjecture by
John Morgan(
Book
)
1 edition published in 2007 in English and held by 278 WorldCat member libraries worldwide
"This book provides full details of a complete proof of the Poincare Conjecture following Perelman's three preprints. After a lengthy introduction that outlines the entire argument, the book is divided into four parts. The first part reviews necessary results from Riemannian geometry and Ricci flow, including much of Hamilton's work. The second part starts with Perelman's length function, which is used to establish crucial noncollapsing theorems. Then it discusses the classification of noncollapsed, ancient solutions to the Ricci flow equation. The third part concerns the existence of Ricci flow with surgery for all positive time and an analysis of the topological and geometric changes introduced by surgery. The last part follows Perelman's third preprint to prove that when the initial Riemannian 3manifold has finite fundamental group, Ricci flow with surgery becomes extinct after finite time. The proofs of the Poincare Conjecture and the closely related 3dimensional spherical spaceform conjecture are then immediate." "With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology."Jacket
1 edition published in 2007 in English and held by 278 WorldCat member libraries worldwide
"This book provides full details of a complete proof of the Poincare Conjecture following Perelman's three preprints. After a lengthy introduction that outlines the entire argument, the book is divided into four parts. The first part reviews necessary results from Riemannian geometry and Ricci flow, including much of Hamilton's work. The second part starts with Perelman's length function, which is used to establish crucial noncollapsing theorems. Then it discusses the classification of noncollapsed, ancient solutions to the Ricci flow equation. The third part concerns the existence of Ricci flow with surgery for all positive time and an analysis of the topological and geometric changes introduced by surgery. The last part follows Perelman's third preprint to prove that when the initial Riemannian 3manifold has finite fundamental group, Ricci flow with surgery becomes extinct after finite time. The proofs of the Poincare Conjecture and the closely related 3dimensional spherical spaceform conjecture are then immediate." "With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology."Jacket
Symplectic 4manifolds and algebraic surfaces : lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September
210, 2003 by
Denis Auroux(
Book
)
21 editions published in 2008 in English and Undetermined and held by 246 WorldCat member libraries worldwide
Modern approaches to the study of symplectic 4manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 210, 2003 will be useful to people working in related areas of mathematics and will become standard references on these topics. The volume is a coherent exposition of an active field of current research focusing on the introduction of new methods for the study of moduli spaces of complex structures on algebraic surfaces, and for the investigation of symplectic topology in dimension 4 and higher
21 editions published in 2008 in English and Undetermined and held by 246 WorldCat member libraries worldwide
Modern approaches to the study of symplectic 4manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 210, 2003 will be useful to people working in related areas of mathematics and will become standard references on these topics. The volume is a coherent exposition of an active field of current research focusing on the introduction of new methods for the study of moduli spaces of complex structures on algebraic surfaces, and for the investigation of symplectic topology in dimension 4 and higher
A mathematician and his mathematical work : selected papers of S.S. Chern by
ShiingShen Chern(
Book
)
9 editions published between 1995 and 1996 in English and held by 171 WorldCat member libraries worldwide
This volume is about the life and work of ShiingShen Chern (1911–), one of the leading mathematicians of this century. The book contains personal accounts by some friends, together with a summary of the mathematical works by Chern himself. Besides a selection of the mathematical papers the book also contains all his papers published after 1988
9 editions published between 1995 and 1996 in English and held by 171 WorldCat member libraries worldwide
This volume is about the life and work of ShiingShen Chern (1911–), one of the leading mathematicians of this century. The book contains personal accounts by some friends, together with a summary of the mathematical works by Chern himself. Besides a selection of the mathematical papers the book also contains all his papers published after 1988
The geometrization conjecture by
John Morgan(
Book
)
1 edition published in 2014 in English and held by 145 WorldCat member libraries worldwide
This book gives a complete proof of the geometrization conjecture, which describes all compact 3manifolds in terms of geometric pieces, i.e., 3manifolds with locally homogeneous metrics of finite volume. The method is to understand the limits as time goes to infinity of Ricci flow with surgery. The first half of the book is devoted to showing that these limits divide naturally along incompressible tori into pieces on which the metric is converging smoothly to hyperbolic metrics and pieces that are locally more and more volume collapsed. The second half of the book is devoted to showing that the latter pieces are themselves geometric. This is established by showing that the GromovHausdorff limits of sequences of more and more locally volume collapsed 3manifolds are Alexandrov spaces of dimension at most 2 and then classifying these Alexandrov spaces. In the course of proving the geometrization conjecture, the authors provide an overview of the main results about Ricci flows with surgery on 3dimensional manifolds, introducing the reader to this difficult material. The book also includes an elementary introduction to GromovHausdorff limits and to the basics of the theory of Alexandrov spaces. In addition, a complete picture of the local structure of Alexandrov surfaces is developed. All of these important topics are of independent interest Provided by publisher
1 edition published in 2014 in English and held by 145 WorldCat member libraries worldwide
This book gives a complete proof of the geometrization conjecture, which describes all compact 3manifolds in terms of geometric pieces, i.e., 3manifolds with locally homogeneous metrics of finite volume. The method is to understand the limits as time goes to infinity of Ricci flow with surgery. The first half of the book is devoted to showing that these limits divide naturally along incompressible tori into pieces on which the metric is converging smoothly to hyperbolic metrics and pieces that are locally more and more volume collapsed. The second half of the book is devoted to showing that the latter pieces are themselves geometric. This is established by showing that the GromovHausdorff limits of sequences of more and more locally volume collapsed 3manifolds are Alexandrov spaces of dimension at most 2 and then classifying these Alexandrov spaces. In the course of proving the geometrization conjecture, the authors provide an overview of the main results about Ricci flows with surgery on 3dimensional manifolds, introducing the reader to this difficult material. The book also includes an elementary introduction to GromovHausdorff limits and to the basics of the theory of Alexandrov spaces. In addition, a complete picture of the local structure of Alexandrov surfaces is developed. All of these important topics are of independent interest Provided by publisher
Ricci flow and the Poincaré conjecture by
John W Morgan(
Book
)
8 editions published in 2007 in English and held by 68 WorldCat member libraries worldwide
8 editions published in 2007 in English and held by 68 WorldCat member libraries worldwide
Transcendental methods in algebraic geometry : lectures given at the 3rd session of the Centro internazionale matematico estivo
(C.I.M.E.) held in Cetraro, Italy, July 412, 1994 by
JeanPierre Demailly(
Book
)
6 editions published between 1996 and 2006 in English and Undetermined and held by 32 WorldCat member libraries worldwide
6 editions published between 1996 and 2006 in English and Undetermined and held by 32 WorldCat member libraries worldwide
Quantum cohomology : lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 30July 8, 1997 by
Kai Behrend(
)
5 editions published between 2002 and 2004 in English and held by 20 WorldCat member libraries worldwide
The book gathers the lectures given at the C.I.M.E. summer school "Quantum Cohomology" held in Cetraro (Italy) from June 30th to July 8th, 1997. The lectures and the subsequent updating cover a large spectrum of the subject on the field, from the algebrogeometric point of view, to the symplectic approach, including recent developments of stringbranes theories and qhypergeometric functions
5 editions published between 2002 and 2004 in English and held by 20 WorldCat member libraries worldwide
The book gathers the lectures given at the C.I.M.E. summer school "Quantum Cohomology" held in Cetraro (Italy) from June 30th to July 8th, 1997. The lectures and the subsequent updating cover a large spectrum of the subject on the field, from the algebrogeometric point of view, to the symplectic approach, including recent developments of stringbranes theories and qhypergeometric functions
The geometrization conjecture by
John Morgan(
Book
)
6 editions published in 2014 in English and held by 15 WorldCat member libraries worldwide
6 editions published in 2014 in English and held by 15 WorldCat member libraries worldwide
The geometrization conjecture by
John Morgan(
Book
)
1 edition published in 2014 in English and held by 15 WorldCat member libraries worldwide
1 edition published in 2014 in English and held by 15 WorldCat member libraries worldwide
Geometry of Kähler metrics and foliations by holomorphic discs by
Xiuxiong X Chen(
Book
)
3 editions published in 2008 in English and held by 10 WorldCat member libraries worldwide
3 editions published in 2008 in English and held by 10 WorldCat member libraries worldwide
Rod bundle heat transfer facility steam cooling with droplet injection experiments data report by
L. E Hochreiter(
Book
)
1 edition published in 2015 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 2015 in English and held by 6 WorldCat member libraries worldwide
Fuel rod performance uncertainty analysis during overpressurization transient for Kuosheng Nuclear Power Plant with TRACE/FRAPTRAN/Dakota
codes in SNAP interface by Chunkuan Shih(
Book
)
1 edition published in 2016 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 2016 in English and held by 4 WorldCat member libraries worldwide
Surveys in geometric analysis 2017 = Ji he fen xi zong shu 2017(
Book
)
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
Fuel rod performance uncertainty analysis during overpressurization transient for Kuosheng Nuclear Power Plant with TRACE/FRAPTRAN/Dakota
codes in SNAP interface by Chunkuan Shih(
Book
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
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Related Identities
 Morgan, John 1946 March 21 Author
 Oh, Y. G.
 Fukaya, K. Author
 Ono, K.
 Mantegazza, Carlo Editor
 Besson, Gérard Other
 Sinestrari, Carlo 1970 Other
 Boileau, Michel Author
 Benedetti, R. Editor
 Catanese, F. (Fabrizio) Other Editor
Useful Links
Associated Subjects
Algebra Algebraic topology Canada Cell aggregationMathematics Chern, ShiingShen, China Complex manifolds Differential equations, Partial Foliations (Mathematics) Functions of complex variables Geometric analysis Geometry Geometry, Algebraic Geometry, Differential Global differential geometry Global Riemannian geometry Group theory Homology theory Hyperbolic groups Isomorphisms (Mathematics) Kählerian manifolds Manifolds (Mathematics) Mathematical physics Mathematicians Mathematics Mirror symmetry Nuclear power plants Nuclear power plantsSafety measures Poincaré conjecture Quantum theory Ricci flow Scientists Sheaf theory Surfaces, Algebraic Symplectic geometry Symplectic groups Symplectic manifolds Taiwan Topological manifolds Topology United States
Covers
Alternative Names
Gang, Tian
Gang Tian Chinees wiskundige
Gang Tian Chinese mathematician
Gang Tian matemático chino
Gang Tian mathématicien chinois
Tian, G.
T'ien, K.
Tʻien, K. 1958
田剛
Languages