Isoperimetric inequalities for quermassintegrals

Neil S. Trudinger

doi:10.1016/S0294-1449(16)30181-0

Isoperimetric inequalities for quermassintegrals

Neil S. Trudinger

Research output: Contribution to journal › Article › peer-review

68 Citations (Scopus)

Abstract

The isoperimetric inequalities of Aleksandrov and Fenchel for quermassintegrals (cross sectional measures) of convex domains in Euclidean space are established for non-convex domains, subject to natural curvature conditions. The techniques are new and draw upon the theory of Monge-Ampère type equations related to previous work of the author on equations of prescribed curvature.

Original language	English
Pages (from-to)	411-425
Number of pages	15
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	11
Issue number	4
DOIs	https://doi.org/10.1016/S0294-1449(16)30181-0
Publication status	Published - 1 Jul 1994

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abstract = "The isoperimetric inequalities of Aleksandrov and Fenchel for quermassintegrals (cross sectional measures) of convex domains in Euclidean space are established for non-convex domains, subject to natural curvature conditions. The techniques are new and draw upon the theory of Monge-Amp{\`e}re type equations related to previous work of the author on equations of prescribed curvature.",

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AB - The isoperimetric inequalities of Aleksandrov and Fenchel for quermassintegrals (cross sectional measures) of convex domains in Euclidean space are established for non-convex domains, subject to natural curvature conditions. The techniques are new and draw upon the theory of Monge-Ampère type equations related to previous work of the author on equations of prescribed curvature.

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ER -

Isoperimetric inequalities for quermassintegrals

Abstract

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