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Intrinsic and extrinsic comparison results for isoperimetric quotients and capacities in weighted manifolds.

Authors :
Hurtado, A.
Palmer, V.
Rosales, C.
Source :
Journal of Mathematical Analysis & Applications. Dec2020, Vol. 492 Issue 2, pN.PAG-N.PAG. 1p.
Publication Year :
2020

Abstract

Let (M , g) be a complete non-compact Riemannian manifold together with a function e h , which weights the Hausdorff measures associated to the Riemannian metric. In this work we assume lower or upper radial bounds on some weighted or unweighted curvatures of M to deduce comparisons for the weighted isoperimetric quotient and the weighted capacity of metric balls in M centered at a point o ∈ M. As a consequence, we obtain parabolicity and hyperbolicity criteria for weighted manifolds generalizing previous ones. A basic tool in our study is the analysis of the weighted Laplacian of the distance function from o. The technique extends to non-compact submanifolds properly immersed in M under certain control on their weighted mean curvature. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
0022247X
Volume :
492
Issue :
2
Database :
Academic Search Index
Journal :
Journal of Mathematical Analysis & Applications
Publication Type :
Academic Journal
Accession number :
145475708
Full Text :
https://doi.org/10.1016/j.jmaa.2020.124488