A Sharp Sobolev Interpolation Inequality on Finsler Manifolds

Kristály, Alexandru (2015) A Sharp Sobolev Interpolation Inequality on Finsler Manifolds. Journal of Geometric Analysis, 25 (4). pp. 2226-2240. ISSN 1050-6926

Text Kristaly_JGA.pdf Restricted to Registered users only Download (238kB) | Request a copy

Abstract

In this paper we study a sharp Sobolev interpolation inequality on Finsler manifolds. We show that Minkowski spaces represent the optimal framework for the Sobolev interpolation inequality on a large class of Finsler manifolds: (1) Minkowski spaces support the sharp Sobolev interpolation inequality; (2) any complete Berwald space with non-negative Ricci curvature which supports the sharp Sobolev interpolation inequality is isometric to a Minkowski space. The proofs are based on properties of the Finsler–Laplace operator and on the Finslerian Bishop–Gromov volume comparison theorem.

Actions (login required)

Edit Item