The first eigenvalue of the p‐Laplace operator under powers of mean curvature flow
The first eigenvalue of the p‐Laplace operator under powers of mean curvature flow
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DOI：
10.1002/mma.2835
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发表时间：
2014-03
影响因子：
2.9
通讯作者：
Liang Zhao
中科院分区：
文献类型：
--
作者：
Liang Zhao
In this paper, we show the following main results. Let (Mn,g(t)), t ∈ [0,T), be a solution of the unnormalized Hk − flow on a closed manifold, and λ1,p(t) be the first eigenvalue of the p‐Laplace operator. If there exists a nonnegative constant ε such that Hkhij−Hk+1pgij≥−εgij in M × [0,T) and Hk+1>pε in M × [0,T),then λ1,p(t) is increasing and the differentiable almost everywhere along the unnormalized Hk − flow on [0,T). At last, we discuss some useful monotonic quantities. Copyright © 2013 John Wiley & Sons, Ltd.
