p-Fundamental tone estimates of submanifolds with bounded mean curvature
- Authors
- Evangelista, Israel; Seo, Keomkyo
- Issue Date
- Apr-2017
- Publisher
- SPRINGER
- Keywords
- p-Laplacian; p-Fundamental tone; Volume growth; Submanifold; Foliation; Bounded mean curvature
- Citation
- ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, v.52, no.3, pp 269 - 287
- Pages
- 19
- Journal Title
- ANNALS OF GLOBAL ANALYSIS AND GEOMETRY
- Volume
- 52
- Number
- 3
- Start Page
- 269
- End Page
- 287
- URI
- https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/8149
- DOI
- 10.1007/s10455-017-9557-1
- ISSN
- 0232-704X
1572-9060
- Abstract
- In this paper, we estimate the p-fundamental tone of submanifolds in a Cartan-Hadamard manifold. First, we obtain lower bounds for the p-fundamental tone of geodesic balls and submanifolds with bounded mean curvature. Moreover, we provide the p-fundamental tone estimates of minimal submanifolds with certain conditions on the norm of the second fundamental form. Finally, we study transversely oriented codimension-one -foliations of open subsets of Riemannian manifolds M and obtain lower bound estimates for the infimum of the mean curvature of the leaves in terms of the p-fundamental tone of .
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