Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 52A40

Retrieve articles in all journals with MSC: 52A40

Additional Information

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