Volume 3, issue 1 (1999)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
The bottleneck conjecture

Greg Kuperberg

Geometry & Topology 3 (1999) 119–135

arXiv: math.MG/9811119

Abstract

The Mahler volume of a centrally symmetric convex body K is defined as M(K) = (VolK)(VolK). Mahler conjectured that this volume is minimized when K is a cube. We introduce the bottleneck conjecture, which stipulates that a certain convex body K K × K has least volume when K is an ellipsoid. If true, the bottleneck conjecture would strengthen the best current lower bound on the Mahler volume due to Bourgain and Milman. We also generalize the bottleneck conjecture in the context of indefinite orthogonal geometry and prove some special cases of the generalization.

Keywords
metric geometry, euclidean geometry, Mahler conjecture, bottleneck conjecture, central symmetry
Mathematical Subject Classification
Primary: 52A40
Secondary: 46B20, 53C99
References
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Publication
Received: 23 November 1998
Accepted: 20 May 1999
Published: 29 May 1999
Proposed: Robion Kirby
Seconded: Walter Neumann, Yasha Eliashberg
Authors
Greg Kuperberg
Department of Mathematics
University of California at Davis
One Shields Avenue
Davis
California 95616
USA