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Parabolicity criteria and characterization results for submanifolds of bounded mean curvature in model manifolds with weights.
- Source :
-
Nonlinear Analysis . Mar2020, Vol. 192, pN.PAG-N.PAG. 1p. - Publication Year :
- 2020
-
Abstract
- Let P be a submanifold properly immersed in a rotationally symmetric manifold having a pole and endowed with a weight e h. The aim of this paper is twofold. First, by assuming certain control on the h -mean curvature of P , we establish comparisons for the h -capacity of extrinsic balls in P , from which we deduce criteria ensuring the h -parabolicity or h -hyperbolicity of P. Second, we employ functions with geometric meaning to describe submanifolds of bounded h -mean curvature which are confined into some regions of the ambient manifold. As a consequence, we derive half-space and Bernstein-type theorems generalizing previous ones. Our results apply for some relevant h -minimal submanifolds appearing in the singularity theory of the mean curvature flow. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MANIFOLDS (Mathematics)
*SYMMETRIC spaces
*SUBMANIFOLDS
*CURVATURE
Subjects
Details
- Language :
- English
- ISSN :
- 0362546X
- Volume :
- 192
- Database :
- Academic Search Index
- Journal :
- Nonlinear Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 141437276
- Full Text :
- https://doi.org/10.1016/j.na.2019.111681