A Sharp Sobolev Interpolation Inequality on Finsler Manifolds

被引：4
|
作者：
Kristaly, Alexandru [1 ,2 ,3 ]
机构：
[1] Univ Babes Bolyai, Dept Econ, Cluj Napoca 400591, Romania
[2] Obuda Univ, Inst Appl Math, H-1034 Budapest, Hungary
[3] Budapest Tech Polytech Inst, H-1034 Budapest, Hungary
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 2015年 / 25卷 / 04期
关键词：
Sobolev interpolation inequality; Sharp constant; Finsler manifold; Minkowski space; Ricci curvature; Rigidity; RIEMANNIAN-MANIFOLDS; HARDY;
D O I：
10.1007/s12220-014-9510-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：2226 / 2240
页数：15
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