This is an announcement for the paper "Local minimality of the volume-product at the simplex" by Jaegil Kim and Shlomo Reisner.

Abstract: It is proved that the simplex is a strict local minimum for the volume-product P(K)=min vol(K)vol(K^z), in the Banach-Mazur space of n-dimensional (classes of ) convex bodies. Here K^z is the polar body of K about the point z and the minimum is taken over all the points z in the interior of K. Linear local stability in the neighborhood of the simplex is proved as well. In the proof, methods that were recently introduced by Nazarov, Petrov, Ryabogin and Zvavitch are extended to the non-symmetric setting.

Archive classification: math.MG math.FA

Mathematics Subject Classification: 52A40

The source file(s), KR-loc-min-simplex.tex: 34954 bytes, is(are) stored in gzipped form as 1001.0217.gz with size 12kb. The corresponding postcript file has gzipped size 84kb.

Submitted from: reisner@math.haifa.ac.il

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http://front.math.ucdavis.edu/1001.0217

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http://arXiv.org/abs/1001.0217

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