期刊
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
卷 15, 期 6, 页码 -出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219199713500119
关键词
Mean curvature flows; self-shrinkers; spheres; the differential operator L and eigenvalues
资金
- JSPS [24340013]
- Grants-in-Aid for Scientific Research [25610016] Funding Source: KAKEN
In this paper, we study eigenvalues of the closed eigenvalue problem of the differential operator L, which is introduced by Colding and Minicozzi in [Generic mean curvature flow I; generic singularities, Ann. Math. 175 (2012) 755-833], on an n-dimensional compact self-shrinker in Rn+p. Estimates for eigenvalues of the differential operator L are obtained. Our estimates for eigenvalues of the differential operator L are sharp. Furthermore, we also study the Dirichlet eigenvalue problem of the differential operator L on a bounded domain with a piecewise smooth boundary in an n-dimensional complete self-shrinker in Rn+p. For Euclidean space R-n, the differential operator L becomes the Ornstein-Uhlenbeck operator in stochastic analysis. Hence, we also give estimates for eigenvalues of the Ornstein-Uhlenbeck operator.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据