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• W2346059305 abstract "Let $(M,g)$ be an $n$-dimensional compact Riemannian manifold ($n>1$) whose metric $g(t)$ evolves by the generalized abstract geometric flow. This paper discusses the evolution, monotonicity and differentiability for the first eigenvalue of the $p$-Laplacian on $(M,g(t))$ with respect to time evolution. We prove that the first nonzero $p$-eigenvalue is monotone nondecreasing along the flow under certain geometric condition and that the first eigenvalue is differentiable almost everywhere. When $p=2$, we recover the corresponding results for the usual Laplace-Beltrami operator. Our results provide a unified approach to the study of $p$-eigenvalue under various geometric flows" @default.
• W2346059305 created "2016-06-24" @default.
• W2346059305 creator A5033412973 @default.
• W2346059305 creator A5040839361 @default.
• W2346059305 date "2016-05-06" @default.
• W2346059305 modified "2023-09-27" @default.
• W2346059305 title "The first eigenvalue of the $p$-Laplacian on time dependent Riemannian metrics" @default.
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• W2346059305 hasPublicationYear "2016" @default.
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