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Necessary conditions and nonexistence results for connected submanifolds in a Riemannian manifold
- Authors
- Seo, Keomkyo
- Issue Date
- Dec-2017
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Minimal submanifold; Bryant surface; Mean curvature; Density estimate; Nonexistence
- Citation
- ADVANCES IN MATHEMATICS, v.321, pp 205 - 220
- Pages
- 16
- Journal Title
- ADVANCES IN MATHEMATICS
- Volume
- 321
- Start Page
- 205
- End Page
- 220
- ISSN
- 0001-8708
1090-2082
- Abstract
- In this paper, we derive density estimates for submanifolds with variable mean curvature in a Riemannian manifold with sectional curvature bounded above by a constant. This leads to distance estimates for the boundaries of compact connected submanifolds. As applications, we give several necessary conditions and nonexistence results for compact connected minimal submanifolds, Bryant surfaces, and surfaces with small L-2 norm of the mean curvature vector in a Riemannian manifold. (c) 2017 Elsevier Inc. All rights reserved.
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