Evolution of the first eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow
发布时间：2021-03-07
点击次数：
- 论文类型：
- 期刊论文
- 发表时间：
- 2021-03-05
- 发表刊物：
- OPEN MATHEMATICS
- 文献类型：
- J
- 卷号：
- 18
- 页面范围：
- 1518-1530
- ISSN号：
- 2391-5455
- 关键字：
- eigenvalue; Laplace operator; p-Laplace operator; monotonicity; forced mean curvature flow
- 摘要：
- In this paper, we discuss the monotonicity of the first nonzero eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow (MCF). By imposing conditions associated with the mean curvature of the initial hypersurface and the coefficient function of the forcing term of a forced MCF, and some special pinching conditions on the second fundamental form of the initial hypersurface, we prove that the first nonzero closed eigenvalues of the Laplace operator and the p-Laplace operator are monotonic under the forced MCF, respectively, which partially generalize Mao and Zhao's work. Moreover, we give an example to specify applications of conclusions obtained above.
- 第一作者
- Qi, Xuesen
- 通讯作者
- 刘西民