Items related to The geometry of domains in space
This treatment of domains in space emphasizes the growing interaction between analysis and geometry. Geometric analysis is an important area of study for both pure and applied mathematicians and engineers.
"synopsis" may belong to another edition of this title.
Review:
"This monograph collects a number of concepts, techniques and results of geometrical nature, centered around the concept of domain, and which are widely used by analysts. This includes the notion of defining functions for a bounded domain, techniques related to the smoothness of the boundary, some measure theory, including rectifiable sets, Minkowski content, covering lemmas, functions with bounded variation, and the area and co-area formula. Then comes a study of the restriction, trace and extension of functions belonging to a Sobolev space. One chapter is devoted to Sard's theorem and its application to the Whitney extension theorem, and another one to convexity and some of its generalizations. Steiner symmetrization is then treated, with its applications to isoperimetric inequalities. The last chapter deals with some questions related to complex analysis, namely quasiconformal mappings and Weyl's theorems on the asymptotic expression of eigenvalues. Two appendices deal with some metrics on the collection of subsets of a Euclidean space and some basic constants associated to those spaces. A short bibliography and an index complete this book, which is clearly written and makes an interesting link between analysis and geometry."
–Zentralblatt Math
"The book can be highly recommended for graduate students as a comprehensive introduction to the field of geometric analysis. Also mathematicians working in other areas can profit a lot from this carefully written book. In particular, the geometric ideas are presented in a self-contained manner; for some of the needed analytic or measure-theoretic results, references are given."
-ZAA
"About this title" may belong to another edition of this title.
- PublisherBirkhauser
- Publication date1999
- ISBN 10 3764340975
- ISBN 13 9783764340971
- BindingHardcover
- Number of pages308
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