Weighted volume growth and vanishing properties of f-minimal hypersurfaces in a weighted manifold
- Authors
- Yun, Gabjin; Seo, Keomkyo
- Issue Date
- Mar-2019
- Publisher
- PERGAMON-ELSEVIER SCIENCE LTD
- Keywords
- f-minimal hypersurface; Weighted manifold; Stability; f-Laplacian; First eigenvalue; Harmonic form
- Citation
- NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v.180, pp 264 - 283
- Pages
- 20
- Journal Title
- NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
- Volume
- 180
- Start Page
- 264
- End Page
- 283
- URI
- https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/3742
- DOI
- 10.1016/j.na.2018.10.015
- ISSN
- 0362-546X
1873-5215
- Abstract
- In this paper, we prove that a complete noncompact submanifold in a weighted manifold with nonpositive sectional curvature has at least linear weighted volume growth. Moreover we obtain several sufficient conditions for f-minimal hypersurfaces to have infinite weighted volume. By using an f-Laplacian comparison result, we obtain a lower bound of the first eigenvalue for the f-Laplace operator on submanifolds in a weighted manifold. We also obtain vanishing results for L-f(2) harmonic 1-forms on complete noncompact f-minimal hypersurfaces in a weighted manifold. Finally we prove a topological structure theorem for complete noncompact L-f-stable f-minimal hypersurfaces via a Liouville-type theorem for f-harmonic functions with finite f-energy. (C) 2018 Elsevier Ltd. All rights reserved.
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