This article is cited in 13 papers

Filling minimality of Finslerian 2-discs

S. V. Ivanov

St. Petersburg Department of the Steklov Mathematical Institute, Russian Academy of Sciences, St. Petersburg, Russia

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 the Holmes–Thompson and Busemann definitions of the Finsler area.

UDC: 514.76

Received in November 2009

Language: English

 English version: Proceedings of the Steklov Institute of Mathematics, 2011, 273, 176–190

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