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

页码：2226 / 2240

页数：15

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