Abstract

Everybody knows what an extreme point of a convex body is. Does this notion have an opposite? A most non-extreme point? Or: can we somehow say that a point is more or less extreme than another? In this paper we show a way to do this. We shall define the notion of moderation for points of a convex body. Then the points of largest moderation will be the moderate, those of smallest moderation the extreme points, as you would expect

Author information

Contact details are reproduced from the original publication and may be historical.

Tudor Zamfirescu

Fachbereich Mathematik, Universität Dortmund, 44221 Dortmund, Germany
and: Institute of Mathematics, Roumanian Academy of Sciences, P.O.B. 1-764, Buchrest 014700, Roumania

tudor.zamfirescu@mathematik.uni-dortmund.de

References

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  2. R. Schneider: Convex Bodies: The Brunn-Minkowski Theory, Cambridge University Press, Cambridge (1993).https://doi.org/10.1017/CBO9780511526282Google Scholar

Suggested citation

J. Itoh, T. Zamfirescu. “Moderation of Convex Bodies.” Journal of Convex Analysis 18 (2011), No. 3, 865–872. https://doi.org/10.68381/jca18054

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press LLC.