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. 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.
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Für Beruf und Forschung
Graduate students and research mathematicians interested in relations between analysis and differential geometry
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ISBN-13
978-0-8218-4060-3 (9780821840603)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
V. I. Burenkov, Cardiff University, United Kingdom; T. Iwaniec, Syracuse University, NY; S. K. Vodopyanov, Sobolev Institute of Mathematics, Novosibirsk, Russia
On an extremal property of quadrilaterals in an Aleksandrov space of curvature $\leq K$ by I. D. Berg and I. G. Nikolaev On boundedness of the fractional maximal operator from complementary Morrey-type spaces to Morrey-type spaces by V. I. Burenkov, H. V. Guliyev, and V. S. Guliyev Generalized condensers and distortion theorems for conformal mappings of planar domains by V. N. Dubinin and D. B. Karp Rearrangement invariant envelopes of generalized Besov, Sobolev, and Calderon spaces by M. L. Goldman Null Lagrangians, the art of integration by parts by T. Iwaniec Geometric measure theory formulas on rectifiable metric spaces by M. Karmanova Stability and regularity of solutions to elliptic systems of partial differential equations by A. P. Kopylov Removable singularities of differential forms and $A$-solutions by V. M. Miklyukov Various generalizations of the volume conjecture by H. Murakami Gradient Young measures and applications to optimal design by P. Pedregal Wavelets for the cochlea by H. M. Reimann Sobolev-type classes of mappings with values in metric spaces by Y. G. Reshetnyak Counterexamples to elliptic regularity and convex integration by L. Szekelyhidi, Jr. Geometry of Carnot-Caratheodory spaces and differentiability of mappings by S. K. Vodopyanov Foundations of the theory of mappings with bounded distortion on Carnot groups by S. K. Vodopyanov.
