Teaching and Research Section of Analysis
Paper
Evolution of the first eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow
Release Time:2021-03-07
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Journal Article
First Author:
Qi, Xuesen
Correspondence Author:
Ximin Liu
Date of Publication:
2021-03-05
Journal:
OPEN MATHEMATICS
Document Type:
J
Volume:
18
Page Number:
1518-1530
ISSN:
2391-5455
Key Words:
eigenvalue; Laplace operator; p-Laplace operator; monotonicity; forced
mean curvature flow
Abstract:
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.