Alexandrov's isodiametric conjecture and the cut locus of a surface
Differential Geometry
2015-12-04 v1
Abstract
We prove that Alexandrov's conjecture relating the area and diameter of a convex surface holds for the surface of a general ellipsoid. This is a direct consequence of a more general result which estimates the deviation from the optimal conjectured bound in terms of the length of the cut locus of a point on the surface. We also prove that the natural extension of the conjecture to general dimension holds among closed convex spherically symmetric Riemannian manifolds. Our results are based on a new symmetrization procedure which we believe to be interesting in its own right.
Keywords
Cite
@article{arxiv.1406.0811,
title = {Alexandrov's isodiametric conjecture and the cut locus of a surface},
author = {Pedro Freitas and David Krejcirik},
journal= {arXiv preprint arXiv:1406.0811},
year = {2015}
}
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16 pages