A spherical surface measure inequality for convex sets

Autor:	Max Jodeit, Charles Fefferman, Michael D. Perlman
Rok vydání:	1972
Předmět:	Convex analysis Unit sphere Convex hull Applied Mathematics General Mathematics Convex curve Mathematical analysis Convex set Convex body Subderivative Orthogonal convex hull Mathematics
Zdroj:	Proceedings of the American Mathematical Society. 33:114-119
ISSN:	1088-6826 0002-9939
DOI:	10.1090/s0002-9939-1972-0293500-1
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::18d28cad9ef72a0759e68f08ea8a9a96 https://doi.org/10.1090/s0002-9939-1972-0293500-1 Zobrazit plný text záznamu