Geometric inequalities

Author(s)

• Burago, I︠U︡. D. (I︠U︡riĭ Dmitrievich)
• Zalgaller, V. A. (Viktor A.)
• Sosinskiĭ, A. B. (Alekseĭ Bronislavovich)

Bibliographic Information

Geometric inequalities

Yu.D. Burago, V.A. Zalgaller ; translated from the Russian by A.B. Sossinsky

（Springer series in Soviet mathematics）（Die Grundlehren der mathematischen Wissenschaften, 285）

Springer-Verlag, c1988

• : U.S.
• : Germany

Other Title

Geometricheskie neravenstva

Note

Originally published: Leningrad : Nauka, 1980

Bibliography: p. [300]-320

Includes indexes

Description and Table of Contents

Description

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.

Table of Contents

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.

by "Nielsen BookData"

Details

• NCID: BA01468704
• ISBN:
  • 0387136150
  • 3540136150
• LCCN: 86010214
• Country Code: gw
• Title Language Code: eng
• Text Language Code: eng
• Original Language Code: rus
• Place of Publication: Berlin ; Tokyo
• Pages/Volumes: xiv, 331 p.
• Size: 24 cm
• Classification:
  • LCC : QA641
  • DC19 : 516.3/6
  • NDC8 : 414.7
• Subject Headings:
  • LCSH : Geometry, Differential
  • LCSH : Isoperimetric inequalities
• Parent Bibliography ID:
  • BA00067956
  • BA00007422