Reshetni︠a︡k, I︠U︡. G. (I︠U︡riĭ Grigorʹevich)
Overview
Works:  84 works in 218 publications in 2 languages and 2,277 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other, Dedicatee 
Classifications:  QA3, 515.9 
Publication Timeline
.
Most widely held works by
I︠U︡. G Reshetni︠a︡k
Geometry IV : nonregular Riemannian geometry by
I︠U︡. G Reshetni︠a︡k(
Book
)
15 editions published between 1993 and 2009 in English and held by 275 WorldCat member libraries worldwide
This volume of the Encyclopaedia contains two articles, which give a survey of modern research into nonregular Riemannian geometry, carried out mostly by Russian mathematicians. The first article written by Reshetnyak is devoted to the theory of twodimensional Riemannian manifolds of bounded curvature. Concepts of Riemannian geometry, such as the area andintegral curvature of a set, and the length and integral curvature of a curve are also defined for these manifolds. Some fundamental results of Riemannian goemetry like the GaussBonnet formula are true in the more general case considered in the book. The second article by Berestovskij and Nikolaev is devoted to the theory of metric spaces whose curvature lies between two given constants. The main result is that these spaces are infact Riemannian. This result has important applications in global Riemanniangeometry. Both parts cover topics, which have not yet been treated in monograph form. Hence the book will be immensely useful to graduate students and researchers in geometry, in particular Riemannian geometry
15 editions published between 1993 and 2009 in English and held by 275 WorldCat member libraries worldwide
This volume of the Encyclopaedia contains two articles, which give a survey of modern research into nonregular Riemannian geometry, carried out mostly by Russian mathematicians. The first article written by Reshetnyak is devoted to the theory of twodimensional Riemannian manifolds of bounded curvature. Concepts of Riemannian geometry, such as the area andintegral curvature of a set, and the length and integral curvature of a curve are also defined for these manifolds. Some fundamental results of Riemannian goemetry like the GaussBonnet formula are true in the more general case considered in the book. The second article by Berestovskij and Nikolaev is devoted to the theory of metric spaces whose curvature lies between two given constants. The main result is that these spaces are infact Riemannian. This result has important applications in global Riemanniangeometry. Both parts cover topics, which have not yet been treated in monograph form. Hence the book will be immensely useful to graduate students and researchers in geometry, in particular Riemannian geometry
Space mappings with bounded distortion by
I︠U︡. G Reshetni︠a︡k(
Book
)
6 editions published between 1982 and 1989 in 3 languages and held by 274 WorldCat member libraries worldwide
6 editions published between 1982 and 1989 in 3 languages and held by 274 WorldCat member libraries worldwide
General theory of irregular curves by
A. D Aleksandrov(
Book
)
11 editions published in 1989 in English and held by 171 WorldCat member libraries worldwide
One service mathematics has rendered the "Et moi ... si j'a\'ait su comment en revenir, human race. It has put common sense back je n'y scrais point alit: Jules Verne where it belongs, on the topmost shelf next to the dusty canister labc\led 'discarded non The series is divergent; therefore we may be sense'. Eric T. 8c\l able to do something with it. O. Hcaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series
11 editions published in 1989 in English and held by 171 WorldCat member libraries worldwide
One service mathematics has rendered the "Et moi ... si j'a\'ait su comment en revenir, human race. It has put common sense back je n'y scrais point alit: Jules Verne where it belongs, on the topmost shelf next to the dusty canister labc\led 'discarded non The series is divergent; therefore we may be sense'. Eric T. 8c\l able to do something with it. O. Hcaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series
Third Siberian School Algebra and Analysis : proceedings of the third Siberian School, Irkutsk State University, Irkutsk,
1989 by
1989, Irkutsk) Siberian School Algebra and Analysis (3(
Book
)
7 editions published in 1995 in English and held by 171 WorldCat member libraries worldwide
7 editions published in 1995 in English and held by 171 WorldCat member libraries worldwide
The Interaction of Analysis and Geometry : International SchoolConference Analysis and Geometry, August 23September 3,
2004, Novosibirsk, Russia by International SchoolConference on Analysis and Geometry(
Book
)
4 editions published in 2007 in English and held by 169 WorldCat member libraries worldwide
"The papers in this volume are based on talks given at the International Conference on Analysis and Geometry in honor of the 75th birthday of Yurii Reshetnyak (Novosibirsk, 2004). The topics include geometry of spaces with bounded curvature in the sense of Alexandrov, quasiconformal mappings and mappings with bounded distortion (quasiregular mappings), nonlinear potential theory, Sobolev spaces, spaces with fractional and generalized smoothness, variational problems, and other modern trends in these areas."Jacket
4 editions published in 2007 in English and held by 169 WorldCat member libraries worldwide
"The papers in this volume are based on talks given at the International Conference on Analysis and Geometry in honor of the 75th birthday of Yurii Reshetnyak (Novosibirsk, 2004). The topics include geometry of spaces with bounded curvature in the sense of Alexandrov, quasiconformal mappings and mappings with bounded distortion (quasiregular mappings), nonlinear potential theory, Sobolev spaces, spaces with fractional and generalized smoothness, variational problems, and other modern trends in these areas."Jacket
Quasiconformal mappings and Sobolev spaces by
V. M Golʹdshteĭn(
Book
)
6 editions published in 1990 in English and held by 158 WorldCat member libraries worldwide
'Ht moi ..., si j'avait su comment en revenir, One lemce mathematics has rendered the je n'y serai. point aile.' human race. It has put common sense back Jule. Verne ... "'" it belong., on the topmost shelf next to the dusty caniller labelled 'discarded non The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'~re of this series
6 editions published in 1990 in English and held by 158 WorldCat member libraries worldwide
'Ht moi ..., si j'avait su comment en revenir, One lemce mathematics has rendered the je n'y serai. point aile.' human race. It has put common sense back Jule. Verne ... "'" it belong., on the topmost shelf next to the dusty caniller labelled 'discarded non The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'~re of this series
Second Siberian Winter School "Algebra and Analysis" : proceedings of the Second Siberian School, Tomsk State University,
Tomsk, 1989 by
1989, Tomsk) Siberian Winter School Algebra and Analysis (2(
Book
)
7 editions published in 1992 in English and held by 150 WorldCat member libraries worldwide
7 editions published in 1992 in English and held by 150 WorldCat member libraries worldwide
Stability theorems in geometry and analysis by
I︠U︡. G Reshetni︠a︡k(
Book
)
6 editions published in 1994 in English and held by 135 WorldCat member libraries worldwide
6 editions published in 1994 in English and held by 135 WorldCat member libraries worldwide
A.D. Alexandrov, selected works by
A. D Aleksandrov(
Book
)
in English and held by 63 WorldCat member libraries worldwide
in English and held by 63 WorldCat member libraries worldwide
Vvedenie v teorii︠u︡ funkt︠s︡iĭ s obobshchennymi proizvodnymi i kvazikonformnye otobrazhenii︠a︡ by
V. M Golʹdshteĭn(
Book
)
4 editions published in 1983 in Russian and held by 24 WorldCat member libraries worldwide
4 editions published in 1983 in Russian and held by 24 WorldCat member libraries worldwide
Nonstandard methods of analysis by
Anatoly G Kusraev(
Book
)
2 editions published in 1990 in Russian and held by 20 WorldCat member libraries worldwide
Nonstandard Methods of Analysis is concerned with the main trends in this field; infinitesimal analysis and Booleanvalued analysis. The methods that have been developed in the last twentyfive years are explained in detail, and are collected in book form for the first time. Special attention is paid to general principles and fundamentals of formalisms for infinitesimals as well as to the technique of descents and ascents in a Booleanvalued universe. The book also includes various novel applications of nonstandard methods to ordered algebraic systems, vector lattices, subdifferentials, convex programming etc. that have been developed in recent years. For graduate students, postgraduates and all researchers interested in applying nonstandard methods in their work
2 editions published in 1990 in Russian and held by 20 WorldCat member libraries worldwide
Nonstandard Methods of Analysis is concerned with the main trends in this field; infinitesimal analysis and Booleanvalued analysis. The methods that have been developed in the last twentyfive years are explained in detail, and are collected in book form for the first time. Special attention is paid to general principles and fundamentals of formalisms for infinitesimals as well as to the technique of descents and ascents in a Booleanvalued universe. The book also includes various novel applications of nonstandard methods to ordered algebraic systems, vector lattices, subdifferentials, convex programming etc. that have been developed in recent years. For graduate students, postgraduates and all researchers interested in applying nonstandard methods in their work
Teoremy ustoĭchivosti v geometrii i analize by
I︠U︡. G Reshetni︠a︡k(
Book
)
7 editions published in 1982 in Russian and held by 20 WorldCat member libraries worldwide
7 editions published in 1982 in Russian and held by 20 WorldCat member libraries worldwide
Different︠s︡ialʹnye uravnenii︠a︡ s chastnymi proizvodnymi : trudy mezhdunarodnoĭ konferent︠s︡ii po different︠s︡ialʹnym uravnenii︠a︡m
s chastnymi proizvodnymi by Mezhdunarodnai︠a︡ konferent︠s︡ii︠a︡ po different︠s︡ialʹnym uravnenii︠a︡m s chastnymi proizvodnymi(
Book
)
2 editions published in 1986 in Russian and held by 19 WorldCat member libraries worldwide
2 editions published in 1986 in Russian and held by 19 WorldCat member libraries worldwide
Ustoĭchivostʹ v Cnorme klassov otobrazheniĭ by
Anatolij Pavlovič Kopylov(
Book
)
3 editions published in 1990 in Russian and held by 18 WorldCat member libraries worldwide
3 editions published in 1990 in Russian and held by 18 WorldCat member libraries worldwide
A.D. Alexandrov, selected works by
A. D Aleksandrov(
Book
)
5 editions published in 1996 in English and held by 18 WorldCat member libraries worldwide
5 editions published in 1996 in English and held by 18 WorldCat member libraries worldwide
Geometry III : theory of surfaces by
I︠U︡. D Burago(
Book
)
4 editions published in 1992 in English and held by 18 WorldCat member libraries worldwide
The theory of twodimensional surfaces in Euclidean spaces is remarkably rich in deep results and applications, for example in the theory of nonlinear partial differential equations, physics and mechanics. This theory has great clarity and intrinsic beauty, and differs in many respects from the theory of multidimensional submanifolds. A separate volume of the Encyclopaedia is therefore devoted to surfaces. It is concerned mainly with the connection between the theory of embedded surfaces and twodimensional Riemannian geometry (and its generalizations), and, above all, with the question of the influence of properties of intrinsic metrics on the geometry of surfaces. In the first article Yu. D. Burago and S.Z. Shefel' give an extended survey of surfaces from a nontraditional viewpoint stressing the connection between classes of metrics and classes of surfaces in En. A number of conjectures are included. The article of E.R. Rozendorn considers the state of the art of the still incomplete theory of the geometry of surfaces of negative curvature in threedimensional Euclidean space, and the article of I. Kh. Sabitov considers subtle questions of local bendability and rigidity ofsurfaces. These articles reflect the development of the results of N.V. Efimov and also include statements of unsolved problems
4 editions published in 1992 in English and held by 18 WorldCat member libraries worldwide
The theory of twodimensional surfaces in Euclidean spaces is remarkably rich in deep results and applications, for example in the theory of nonlinear partial differential equations, physics and mechanics. This theory has great clarity and intrinsic beauty, and differs in many respects from the theory of multidimensional submanifolds. A separate volume of the Encyclopaedia is therefore devoted to surfaces. It is concerned mainly with the connection between the theory of embedded surfaces and twodimensional Riemannian geometry (and its generalizations), and, above all, with the question of the influence of properties of intrinsic metrics on the geometry of surfaces. In the first article Yu. D. Burago and S.Z. Shefel' give an extended survey of surfaces from a nontraditional viewpoint stressing the connection between classes of metrics and classes of surfaces in En. A number of conjectures are included. The article of E.R. Rozendorn considers the state of the art of the still incomplete theory of the geometry of surfaces of negative curvature in threedimensional Euclidean space, and the article of I. Kh. Sabitov considers subtle questions of local bendability and rigidity ofsurfaces. These articles reflect the development of the results of N.V. Efimov and also include statements of unsolved problems
Prostranstvennye otobrazhenii︠a︡ s ogranichennym iskazheniem by
I︠U︡. G Reshetni︠a︡k(
Book
)
2 editions published in 1982 in Russian and held by 16 WorldCat member libraries worldwide
2 editions published in 1982 in Russian and held by 16 WorldCat member libraries worldwide
Vektornye reshetki i integralʹnye operatory by
I︠U︡. G Reshetni︠a︡k(
Book
)
3 editions published in 1992 in Russian and held by 16 WorldCat member libraries worldwide
3 editions published in 1992 in Russian and held by 16 WorldCat member libraries worldwide
Issledovanii︠a︡ po geometrii i matematicheskomu analizu(
Book
)
3 editions published in 1987 in Russian and held by 13 WorldCat member libraries worldwide
3 editions published in 1987 in Russian and held by 13 WorldCat member libraries worldwide
Stability theorems in geometry and analysis by
I︠U︡. G Reshetni︠a︡k(
Book
)
6 editions published between 1994 and 2011 in English and held by 3 WorldCat member libraries worldwide
This is one of the first monographs to deal with the metric theory of spatial mappings and incorporates results in the theory of quasiconformal, quasiisometric and other mappings. The main subject is the study of the stability problem in Liouville's theorem on conformal mappings in space
6 editions published between 1994 and 2011 in English and held by 3 WorldCat member libraries worldwide
This is one of the first monographs to deal with the metric theory of spatial mappings and incorporates results in the theory of quasiconformal, quasiisometric and other mappings. The main subject is the study of the stability problem in Liouville's theorem on conformal mappings in space
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Related Identities
 Aleksandrov, A. D. (Aleksandr Danilovich) 19121999 Author
 Bokutʹ, L. A. (Leonid Arkadʹevich) 1937 Editor
 Golʹdshteĭn, V. M. (Vladimir Mikhaĭlovich) Author
 Vodopʹi︠a︡nov, S. K. (Sergeĭ Konstantinovich) Editor
 Burenkov, Victor I. 1941 Editor
 Iwaniec, Tadeusz Editor
 Hazewinkel, Michiel Editor
 Kutateladze, S. S. (Semen Samsonovich) Other Editor
 Aleksandrov, I. A. (Igorʹ Aleksandrovich) (Mathematician) Other Editor
 Gamkrelidze, R.V. Editor
Useful Links
Associated Subjects
Algebra Conformal mapping Curves on surfaces Differential equations Differential equations, Partial Engineering mathematics Functional analysis Functional equations Functions Geometry Geometry, Analytic Geometry, Differential Geometry, Riemannian Global analysis (Mathematics) Global differential geometry Integral equations Integral operators Integral transforms Logic, Symbolic and mathematical Mappings (Mathematics) Mathematical analysis Mathematical optimization Mathematics Nonstandard mathematical analysis Quasiconformal mappings Reshetni︠a︡k, I︠U︡. G.(I︠U︡riĭ Grigorʹevich) Riesz spaces Stability Surfaces Topological groups Topology
Alternative Names
Jurij Resjetnjak
Juriy Grigorevitsj Resjetnjak Russisch wiskundige
Rechetniak Iourï Grigorevitch
Rešetnâk, Û. G.
Rešetnjak, Ju. G.
Rešetnjak, Jurij Grigor'evič
Rešetnjak, Jurij Grigor'evič. [t]
Reshetni︠a︡k, I︠U︡. G.
Reshetniak Iurî Grigorʹevich
Reshetni︠a︡k, I︠U︡riĭ Grigorʹevich
Reshetnyak Yu. G.
Reshetnyak, Yurii
Yurii Reshetnyak
Yurii Reshetnyak Soviet Russian mathematician
Γιούρι Ρεσέτνιακ
Решетняк, Ю. Г..
Решетняк, Ю. Г. (Юрий Григорьевич)
Решетняк, Юрий Григорьевич
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