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Geometric Inequalities : Grundlehren Der Mathematischen Wissenschaften - Yurii D. Burago

Geometric Inequalities

Grundlehren Der Mathematischen Wissenschaften

Hardcover Published: 22nd January 1988
ISBN: 9783540136156
Number Of Pages: 334

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Geometrie inequalities have a wide range of applieations-within geometry itself as weIl as beyond its limits. The theory of funetions of a eomplex variable, the ealculus of variations in the large, embedding theorems of funetion spaees, a priori estimates for solutions of differential equations yield many sueh examples. We have attempted to piek out the most general inequalities and, in model eases, we exhibit effeetive geometrie eonstruetions and the means of proving sueh inequalities. A substantial part of this book deals with isoperimetrie inequalities and their generalizations, but, for all their variety, they do not exhaust the eontents ofthe book. The objeets under eonsideration, as a rule, are quite general. They are eurves, surfaees and other manifolds, embedded in an underlying space or supplied with an intrinsie metrie. Geometrie inequalities, used for different purposes, appear in different eontexts-surrounded by a variety ofteehnieal maehinery, with diverse require- ments for the objeets under study. Therefore the methods of proof will differ not only from ehapter to ehapter, but even within individual seetions. An inspeetion of monographs on algebraie and funetional inequalities ([HLP], [BeB], [MV], [MM]) shows that this is typical for books of this type.

1. Two-Dimensional Surfaces.- 2. The Brunn-Minkowski Inequality and the Classical Isoperimetric Inequality.- 3. Isoperimetric Inequalities for Various Definitions of Area.- 4. Mixed Volumes.- 5. Immersions in ?n.- 6. Riemannian Manifolds.- Author Index.

ISBN: 9783540136156
ISBN-10: 3540136150
Series: Grundlehren Der Mathematischen Wissenschaften
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 334
Published: 22nd January 1988
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 2.0
Weight (kg): 0.67