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Indexed by:期刊论文

Date of Publication:2021-03-05

Journal:OPEN MATHEMATICS

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.