✦ LIBER ✦

On the volume of convex hulls of sets on spheres

✍ Scribed by Rafał LatałA; Marek Pycia

Publisher: Springer
Year: 1996
Tongue: English
Weight: 198 KB
Volume: 63
Category: Article
ISSN: 0046-5755
DOI: 10.1007/bf00148215

No coin nor oath required. For personal study only.

✦ Synopsis

We prove that for a measurable subset of S '~-J 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.

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