The Geometry of Domains in Space

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Overview

This comprehensive treatment of domains (in space) emphasizes the growing interaction between analysis and geometry. Geometric analysis, as it is known, is currently an important area of study for both pure and applied mathematicians, physicists, and engineers. Aimed at graduate students of the field, this monograph will be useful in the classroom or as a resource for self-study. The prerequisites are minimal; a good understanding of multivariable calculus and linear algebra ...
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Hardcover (1999)
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Overview

This comprehensive treatment of domains (in space) emphasizes the growing interaction between analysis and geometry. Geometric analysis, as it is known, is currently an important area of study for both pure and applied mathematicians, physicists, and engineers. Aimed at graduate students of the field, this monograph will be useful in the classroom or as a resource for self-study. The prerequisites are minimal; a good understanding of multivariable calculus and linear algebra will suffice for most purposes.
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Product Details

Table of Contents

Preface
1 Elementary Topics 1
2 Domains with Smooth Boundaries 27
3 Measures 57
4 Sobolev Spaces 143
5 Smooth Mappings 157
6 Convexity 191
7 Steiner Symmetrization 223
8 Topics Related to Complex Analysis 247
A.1 Metrics on the Collection of Subsets of Euclidean Space 275
A.2 The Constants Associated to Euclidean Space 281
Guide to Notation 287
Bibliography 291
Index 305
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