**Contemporary Mathematics**

Volume: 424;
2007;
344 pp;
Softcover

MSC: Primary 26; 28; 30; 35; 46; 49; 53; 57; 58;

**Print ISBN: 978-0-8218-4060-3
Product Code: CONM/424**

List Price: $112.00

AMS Member Price: $89.60

MAA Member Price: $100.80

**Electronic ISBN: 978-0-8218-8103-3
Product Code: CONM/424.E**

List Price: $105.00

AMS Member Price: $84.00

MAA Member Price: $94.50

# The Interaction of Analysis and Geometry

Share this page *Edited by *
*V. I. Burenkov; T. Iwaniec; S. K. Vodopyanov*

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 Yuri&ibreve; 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.

#### Readership

Graduate students and research mathematicians interested in relations between analysis and differential geometry.

# Table of Contents

## The Interaction of Analysis and Geometry

- Contents v6 free
- Preface vii8 free
- On an extremal property of quadrilaterals in an Aleksandrov space of curvature ≤ K 110 free
- On boundedness of the fractional maximal operator from complementary Morrey-type spaces to Morrey-type spaces 1726
- Generalized condensers and distortion theorems for conformal mappings of planar domains 3342
- Rearrangement invariant envelopes of generalized Besov, Sobolev, and Calderon spaces 5362
- Null Lagrangians, the art of integration by parts 8392
- Geometric measure theory formulas on rectifiable metric spaces 103112
- Stability and regularity of solutions to elliptic systems of partial differential equations 137146
- Gradient Young measures and applications to optimal design 187196
- Wavelets for the cochlea 201210
- Sobolev-type classes of mappings with values in metric spaces 209218
- Counterexamples to elliptic regularity and convex integration 227236
- Geometry of Carnot–Carathéodory spaces and differentiability of mappings 247256
- Foundations of the theory of mappings with bounded distortion on Carnot groups 303312