Evolution of the first eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow,Open Mathematics

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Evolution of the first eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow
Open Mathematics ( IF 1.0 ) Pub Date : 2020-01-01 , DOI: 10.1515/math-2020-0090
Xuesen Qi ₁ , Ximin Liu ₁

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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.

更新日期：2020-01-01

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