On the Volume of Convex Hulls of Sets on Spheres

Authors: LATALA R.¹; PYCIA M.¹

Source: Geometriae Dedicata, Volume 63, Number 2, November 1996 , pp. 153-157(5)

Publisher: Springer

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Abstract:

We prove that for a measurable subset of S^{n-1}<\math> with fixed Haar measure, the volume of its convex hull is minimized for a cap (i.e. a ball with respect to the geodesic measure). We solve a similar problem for symmetric sets and $n=2,3. As a consequence, we deduce a result concerning Gaussian measures of dilatations of convex, symmetric sets in R^{2} and R^{3}.$

Keywords: isoperimetry; Gaussian measures; convex hull

Language: English

Document Type: Regular paper

Affiliations: 1: Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland. e-mail: rlatala@mimuw.edu.pl, mpycia@mimuw.edu.pl

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