Dual spheres have the same girth
Metric Geometry
2011-09-21 v1 Symplectic Geometry
Abstract
Symplectic and Finsler geometry are used to settle a conjecture of Sch\"affer stating that the girth of a normed space--the infimum of the lengths of all closed, rectifiable, centrally symmetric curves on its unit sphere--equals the girth of its dual.
Cite
@article{arxiv.math/0408414,
title = {Dual spheres have the same girth},
author = {Juan Carlos Alvarez Paiva},
journal= {arXiv preprint arXiv:math/0408414},
year = {2011}
}
Comments
10 pages