A Sharp Sobolev Interpolation Inequality on Finsler Manifolds

作者：Kristaly Alexandru^*

来源：Journal of Geometric Analysis, 2015, 25(4): 2226-2240.

DOI：10.1007/s12220-014-9510-5

• Sobolev interpolation inequality
• Sharp constant
• Finsler manifold
• Minkowski space
• Ricci curvature
• Rigidity

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.

• 出版日期2015-10