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The Interaction of Analysis and Geometry

Edited by: V. I. Burenkov Cardiff University, Cardiff, United Kingdom
T. Iwaniec Syracuse University, Syracuse, NY
S. K. Vodopyanov Sobolev Institute of Mathematics, Novosibirsk, Russia
Available Formats:
Electronic ISBN: 978-0-8218-8103-3
Product Code: CONM/424.E
List Price: $105.00 MAA Member Price:$94.50
AMS Member Price: $84.00 Click above image for expanded view The Interaction of Analysis and Geometry Edited by: V. I. Burenkov Cardiff University, Cardiff, United Kingdom T. Iwaniec Syracuse University, Syracuse, NY S. K. Vodopyanov Sobolev Institute of Mathematics, Novosibirsk, Russia Available Formats:  Electronic ISBN: 978-0-8218-8103-3 Product Code: CONM/424.E  List Price:$105.00 MAA Member Price: $94.50 AMS Member Price:$84.00
• Book Details

Contemporary Mathematics
Volume: 4242007; 344 pp
MSC: 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.

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 Morrey-type spaces to Morrey-type 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 - Sobolev-type 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 Carnot-Carathéodory 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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Volume: 4242007; 344 pp
MSC: 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.

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 Morrey-type spaces to Morrey-type 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 - Sobolev-type 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 Carnot-Carathéodory 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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