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Product Code:  CONM/424.E 
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Book DetailsContemporary MathematicsVolume: 424; 2007; 344 ppMSC: Primary 26; 28; 30; 35; 46; 49; 53; 57; 58;
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 Yuriĭ 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. Most articles are related to Reshetnyak's original works and demonstrate the vitality of his fundamental contribution in some important fields of mathematics such as the geometry in the "large", quasiconformal analysis, Sobolev spaces, potential theory and variational calculus.
ReadershipGraduate students and research mathematicians interested in relations between analysis and differential geometry.

Table of Contents

Articles

I. D. Berg and I. G. Nikolaev  On an extremal property of quadrilaterals in an Aleksandrov space of curvature $\leq K$ [ MR 2316328 ]

V. I. Burenkov, H. V. Guliyev and V. S. Guliyev  On boundedness of the fractional maximal operator from complementary Morreytype spaces to Morreytype spaces [ MR 2316329 ]

V. N. Dubinin and D. B. Karp  Generalized condensers and distortion theorems for conformal mappings of planar domains [ MR 2316330 ]

M. L. Goldman  Rearrangement invariant envelopes of generalized Besov, Sobolev, and Calderon spaces [ MR 2316331 ]

Tadeusz Iwaniec  Null Lagrangians, the art of integration by parts [ MR 2316332 ]

Maria Karmanova  Geometric measure theory formulas on rectifiable metric spaces [ MR 2316333 ]

A. P. Kopylov  Stability and regularity of solutions to elliptic systems of partial differential equations [ MR 2316334 ]

V. M. Miklyukov  Removable singularities of differential forms and $A$solutions [ MR 2316335 ]

Hitoshi Murakami  Various generalizations of the volume conjecture [ MR 2316336 ]

P. Pedregal  Gradient Young measures and applications to optimal design [ MR 2316337 ]

H. M. Reimann  Wavelets for the cochlea [ MR 2316338 ]

Yu. G. Reshetnyak  Sobolevtype classes of mappings with values in metric spaces [ MR 2316339 ]

László Székelyhidi, Jr.  Counterexamples to elliptic regularity and convex integration [ MR 2316340 ]

S. K. Vodopyanov  Geometry of CarnotCarathéodory spaces and differentiability of mappings [ MR 2316341 ]

S. K. Vodopyanov  Foundations of the theory of mappings with bounded distortion on Carnot groups [ MR 2316342 ]


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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 Yuriĭ 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. Most articles are related to Reshetnyak's original works and demonstrate the vitality of his fundamental contribution in some important fields of mathematics such as the geometry in the "large", quasiconformal analysis, Sobolev spaces, potential theory and variational calculus.
Graduate students and research mathematicians interested in relations between analysis and differential geometry.

Articles

I. D. Berg and I. G. Nikolaev  On an extremal property of quadrilaterals in an Aleksandrov space of curvature $\leq K$ [ MR 2316328 ]

V. I. Burenkov, H. V. Guliyev and V. S. Guliyev  On boundedness of the fractional maximal operator from complementary Morreytype spaces to Morreytype spaces [ MR 2316329 ]

V. N. Dubinin and D. B. Karp  Generalized condensers and distortion theorems for conformal mappings of planar domains [ MR 2316330 ]

M. L. Goldman  Rearrangement invariant envelopes of generalized Besov, Sobolev, and Calderon spaces [ MR 2316331 ]

Tadeusz Iwaniec  Null Lagrangians, the art of integration by parts [ MR 2316332 ]

Maria Karmanova  Geometric measure theory formulas on rectifiable metric spaces [ MR 2316333 ]

A. P. Kopylov  Stability and regularity of solutions to elliptic systems of partial differential equations [ MR 2316334 ]

V. M. Miklyukov  Removable singularities of differential forms and $A$solutions [ MR 2316335 ]

Hitoshi Murakami  Various generalizations of the volume conjecture [ MR 2316336 ]

P. Pedregal  Gradient Young measures and applications to optimal design [ MR 2316337 ]

H. M. Reimann  Wavelets for the cochlea [ MR 2316338 ]

Yu. G. Reshetnyak  Sobolevtype classes of mappings with values in metric spaces [ MR 2316339 ]

László Székelyhidi, Jr.  Counterexamples to elliptic regularity and convex integration [ MR 2316340 ]

S. K. Vodopyanov  Geometry of CarnotCarathéodory spaces and differentiability of mappings [ MR 2316341 ]

S. K. Vodopyanov  Foundations of the theory of mappings with bounded distortion on Carnot groups [ MR 2316342 ]