Geometric inequalities
著者
書誌事項
Geometric inequalities
（Springer series in Soviet mathematics）（Die Grundlehren der mathematischen Wissenschaften, 285）
Springer-Verlag, c1988
- : U.S.
- : Germany
- タイトル別名
-
Geometricheskie neravenstva
大学図書館所蔵 件 / 全95件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Originally published: Leningrad : Nauka, 1980
Bibliography: p. [300]-320
Includes indexes
内容説明・目次
内容説明
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.
目次
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.
「Nielsen BookData」 より