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Necessary conditions and nonexistence results for connected submanifolds in a Riemannian manifold
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1초록
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.
키워드
Minimal submanifold; Bryant surface; Mean curvature; Density estimate; Nonexistence; BOUNDED MEAN-CURVATURE; MINIMAL-SURFACES; MAXIMUM-PRINCIPLES; ISOPERIMETRIC-INEQUALITIES
- 제목
- Necessary conditions and nonexistence results for connected submanifolds in a Riemannian manifold
- 저자
- Seo, Keomkyo
- 발행일
- 2017-12
- 유형
- Article
- 권
- 321
- 페이지
- 205 ~ 220