The bottleneck conjecture

Details The bottleneck conjecture The bottleneck conjecture

1998-11-19

arxiv.org/abs/math/9811119v2

Geom. Topol. 3 (1999), 119-135

Mathematics

Metric Geometry

17 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper5.abs.html

Scientific paper

The Mahler volume of a centrally symmetric convex body K is defined as M(K)= (Vol K)(Vol K^dual). 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^diamond subset K X K^dual 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.

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