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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A spherical surface measure inequality for convex sets


Authors: Charles Fefferman, Max Jodeit and Michael D. Perlman
Journal: Proc. Amer. Math. Soc. 33 (1972), 114-119
MSC: Primary 52A40
MathSciNet review: 0293500
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0293500-1
PII: S 0002-9939(1972)0293500-1
Keywords: Symmetric convex sets, geometric inequality, hypersurface area, second derivative test, radial measure, symmetric distributions, scale parameter family
Article copyright: © Copyright 1972 American Mathematical Society