Dimensions at Infinity for Riemannian Manifolds

Thierry Coulhon
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Thierry Coulhon: Université de Cergy-Pontoise, Département de Mathématiques

A chapter in Potential Theory and Degenerate Partial Differential Operators, 1995, pp 335-344 from Springer

Abstract: Abstract This paper is essentially a survey, with however some variations or new points of view on already published results. The main theme is the study of the relationship between various Sobolev type inequalities on manifolds. In the first part, we introduce a scale of dimensions at infinity adapted to manifolds of polynomial growth, in which we recast the results of [C2], [BCLS], and [CL]. In the second one, we show how Poincaré inequalities allow at the same time to go down in the scale and to refine it into a scale of global inequalities ([CS2], [S], [C2]). In the third part, we take up the more general situation where the volume growth of the manifold is not necessarily governed by a power function.

Keywords: RIEMANNIAN Manifold; Heat Kernel; Ricci Curvature; Finite Subset; Isoperimetric Inequality (search for similar items in EconPapers)
Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-011-0085-4_3

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DOI: 10.1007/978-94-011-0085-4_3

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