Geometric Inequalities: 285 (Grundlehren der mathematischen Wissenschaften) - Hardcover

Burago, Yurii D.; Zalgaller, Viktor A.

 
9783540136156: Geometric Inequalities: 285 (Grundlehren der mathematischen Wissenschaften)
Hardcover
ISBN 10: 3540136150 ISBN 13: 9783540136156
Verlag: Springer, 1988

Inhaltsangabe

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.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Reseña del editor

A 1988 classic, covering Two-dimensional Surfaces; Domains on the Plane and on Surfaces; Brunn-Minkowski Inequality and Classical Isoperimetric Inequality; Isoperimetric Inequalities for Various Definitions of Area; and Inequalities Involving Mean Curvature.

Reseña del editor

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.

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Verlag
Springer
Erscheinungsdatum
1988
Sprache
Englisch
ISBN 10 
3540136150
ISBN 13 
9783540136156
Einband
Tapa dura
Anzahl der Seiten
356
Kontakt zum Hersteller
Nicht verfügbar
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ISBN 10:  3642057241 ISBN 13:  9783642057243
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Softcover