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Mat. Zametki, 2001, Volume 69, Issue 2, Pages 171–180 (Mi mz493)  

Realization of Configurations and the Loewner Ellipsoid

S. A. Bogatyi

M. V. Lomonosov Moscow State University

Abstract: It is proved that any subset of an $(m-1)$-dimensional sphere of volume larger than $l(m+1)$ of the volume of the entire sphere contains $l+1$ points forming a regular $l$-dimensional simplex. As a corollary, it is obtained that, if the exterior of a given $m$-dimensional filled ellipsoid contains no more than the $1/(m+1)$ fraction of some sphere, then the volume of the ellipsoid is no less than the volume of the corresponding ball. The existence of a pair of points a given spherical distance apart in a set of positive measure is examined.

DOI: https://doi.org/10.4213/mzm493

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English version:
Mathematical Notes, 2001, 69:2, 149–157

Bibliographic databases:

UDC: 514.177
Received: 03.03.1999

Citation: S. A. Bogatyi, “Realization of Configurations and the Loewner Ellipsoid”, Mat. Zametki, 69:2 (2001), 171–180; Math. Notes, 69:2 (2001), 149–157

Citation in format AMSBIB
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