Free boundary stable hypersurfaces in manifolds with density and rigidity results

JOURNAL OF GEOMETRY AND PHYSICS

卷:79

Article

Castro, Katherine¹  Rosales, Cesar¹ 

[1] Univ Granada, Dept Geometria & Topol, E-18071 Granada, Spain

关键词: Manifolds with density;    Free boundary;    Mean curvature;    Stability;    Rigidity;   

DOI  :  10.1016/j.geomphys.2014.01.013

来源: Elsevier

【 摘 要 】

Let M be a weighted manifold with boundary partial derivative M, i.e., a Riemannian manifold where a density function is used to weight the Riemannian Hausdorff measures. In this paper we compute the first and second variational formulas of the interior weighted area for deformations by hypersurfaces with boundary in partial derivative m. As a consequence, we obtain variational characterizations of critical points and second order minima of the weighted area with or without a volume constraint. Moreover, in the compact case, we obtain topological estimates and rigidity properties for free boundary stable and area-minimizing hypersurfaces under certain curvature and boundary assumptions on M. Our results and proofs extend previous ones for Riemannian manifolds (constant densities) and for hypersurfaces with empty boundary in weighted manifolds. (C) 2014 Elsevier BM. All rights reserved.

【 授权许可】

Free