A Sharp Sobolev Interpolation Inequality on Finsler Manifolds
Létrehozó:
Kristály, Alexandru
Dátum:
2015
Téma:
QA Mathematics / matematika
QA73 Geometry / geometria
QA74 Analysis / analízis
Tartalmi leírás:
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.
Kristály, Alexandru (2015) A Sharp Sobolev Interpolation Inequality on Finsler Manifolds. Journal of Geometric Analysis, 25 (4). pp. 2226-2240. ISSN 1050-6926
