A spherical surface measure inequality for convex sets

Charles Fefferman, Max Jodeit, Michael D. Perlman

Research output: Contribution to journalArticle

9 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 languageEnglish (US)
Pages (from-to)114-119
Number of pages6
JournalProceedings of the American Mathematical Society
Volume33
Issue number1
DOIs
StatePublished - May 1972
Externally publishedYes

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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