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On the product of distances to a point set on a sphere

Part of: Probabilistic theory: distribution modulo $1$; metric theory of algorithms General convexity

Published online by Cambridge University Press:  09 April 2009

Gerold Wagner
Gerold Wagner
Affiliation:
Mathematisches Institut APfaffenwaldring 57 D-7000 Stuttgart 80 Federal Republic of, Germany
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Abstract

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Let S be the surface of the unit sphere in three-dimensional euclidean space, and let WN=(x1x2, xN)be an N-tuple of points on S. We consider the product of mutual distances and, for the variable point x on S, the product of distance from x to the points of ωN. We obtain essentially best possible bounds for maxωN p(ΩN) and for minωN maxx∈sp(x, ωN).

MSC classification

Secondary: 11K38: Irregularities of distribution, discrepancy 52A40: Inequalities and extremum problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 3 , December 1989 , pp. 466 - 482
Copyright
Copyright © Australian Mathematical Society 1989

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