A spherical surface measure inequality for convex sets

Charles Fefferman; Max Jodeit; Michael D. Perlman

doi:10.1090/S0002-9939-1972-0293500-1

A spherical surface measure inequality for convex sets

Charles Fefferman, Max Jodeit, Michael D. Perlman

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

11 Scopus citations

Abstract

Let the set C in the Euclidean space of.n dimensions be closed, symmetric under reflection in the origin, and convex. The portion of the surface of the unit ball lying in C is shown to decrease in (the uniform) surface measure when C is replaced by AC, the image of C under any linear transformation A with norm no greater than one. Some cases of equality are discussed, and an application is given.

Original language	English (US)
Pages (from-to)	114-119
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	33
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1972-0293500-1
State	Published - May 1972
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

Keywords

Geometric inequality
Hypersurface area
Radial measure
Scale parameter family
Second derivative test
Symmetric convex sets
Symmetric distributions

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10.1090/S0002-9939-1972-0293500-1

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AU - Jodeit, Max

AU - Perlman, Michael D.

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AB - Let the set C in the Euclidean space of.n dimensions be closed, symmetric under reflection in the origin, and convex. The portion of the surface of the unit ball lying in C is shown to decrease in (the uniform) surface measure when C is replaced by AC, the image of C under any linear transformation A with norm no greater than one. Some cases of equality are discussed, and an application is given.

KW - Geometric inequality

KW - Hypersurface area

KW - Radial measure

KW - Scale parameter family

KW - Second derivative test

KW - Symmetric convex sets

KW - Symmetric distributions

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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ER -

A spherical surface measure inequality for convex sets

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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