Filling minimality of Finslerian 2-discs

Details Filling minimality of Finslerian 2-discs Filling minimality of Finslerian 2-discs

2009-10-13

arxiv.org/abs/0910.2257v2

Proc. Steklov Inst. Math. 273 (2011), 176-190

Mathematics

Differential Geometry

16 pages, v2: improved introduction and formatting

Scientific paper

10.1134/S0081543811040079

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.

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