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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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 No.:
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.
Translation or Not:
no
