Geometry & Topology 3 (1999) 119–135

DOI: 10.2140/gt.1999.3.119

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