Evolution of the first eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow
Keyword(s):
The Mean
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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.
2012 ◽
Vol 63
(3-4)
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pp. 937-948
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2020 ◽
Vol 102
(1)
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pp. 162-171
2013 ◽
Vol 37
(5)
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pp. 744-751
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2010 ◽
Vol 53
(7)
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pp. 1703-1710
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2018 ◽
Vol 62
(9)
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pp. 1793-1798
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