Volume 3, issue 1 (1999)

Download this article
For printing
Recent Issues

Volume 26
Issue 8, 3307–3833
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
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
Forward citations
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