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Polytopes of Maximal Volume Product Zvavitch, Artem Mar 26, 2018

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Title Polytopes of Maximal Volume Product
Creator Zvavitch, Artem
Publisher Banff International Research Station for Mathematical Innovation and Discovery
Date Issued 2018-03-26T15:51
Description For a convex body $K \subset \R^n$, let $$K^z = \{y\in \R^n : \langle y-z, x-z\rangle\le 1, \mbox{\ for all\ } x\in K\}$$ be the polar body of $K$ with respect to the center of polarity $z \in \R^n$. In this talk we would like to discuss the maximum of the volume product $$\mathcal{P}(K)=\min_{z\in {\rm int}(K)}|K||K^z|,$$ among convex polytopes $K\subset {\mathbb R}^n$ with a number of vertices bounded by some fixed integer $m \ge n+1$. In particular, we will show that the supremum is reached at a simplicial polytope with exactly $m$ vertices and we provide a new proof of a result of Meyer and Reisner showing that, in the plane, the regular polygon has maximal volume product among all polygons with at most $m$ vertices.
Extent 27 minutes
Subject Mathematics
Functional analysis
Convex and discrete geometry
Geographic Location Banff (Alta.)
Type Moving Image
FileFormat video/mp4
Language eng
Notes Author affiliation: Kent State University
Series BIRS Workshop Lecture Videos (Banff, Alta)
Date Available 2018-09-23
Provider Vancouver : University of British Columbia Library
Rights Attribution-NonCommercial-NoDerivatives 4.0 International
DOI 10.14288/1.0372137
URI http://hdl.handle.net/2429/67232
Affiliation Non UBC
Peer Review Status Unreviewed
Scholarly Level Faculty
Rights URI http://creativecommons.org/licenses/by-nc-nd/4.0/
AggregatedSourceRepository DSpace

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48630-201803261551-Zvavitch_lrv.mp4 [ 101.5MB ]
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48630-1.0372137.ris

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