Filling minimality of Finslerian 2-discs
Differential Geometry
2011-10-03 v2 Metric Geometry
Abstract
We prove that every Riemannian metric on the 2-disc such that all its geodesics are minimal, is a minimal filling of its boundary (within the class of fillings homeomorphic to the disc). This improves an earlier result of the author by removing the assumption that the boundary is convex. More generally, we prove this result for Finsler metrics with area defined as the two-dimensional Holmes-Thompson volume. This implies a generalization of Pu's isosystolic inequality to Finsler metrics, both for Holmes-Thompson and Busemann definitions of Finsler area.
Keywords
Cite
@article{arxiv.0910.2257,
title = {Filling minimality of Finslerian 2-discs},
author = {Sergei Ivanov},
journal= {arXiv preprint arXiv:0910.2257},
year = {2011}
}
Comments
16 pages, v2: improved introduction and formatting