The First Eigenvalue of p-Laplace Operator Under Powers of the mth Mean Curvature Flow
The First Eigenvalue of p-Laplace Operator Under Powers of the mth Mean Curvature Flow
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DOI：
10.1007/s00025-012-0242-1
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发表时间：
2013-06
影响因子：
2.2
通讯作者：
Liang Zhao
中科院分区：
文献类型：
--
作者：
Liang Zhao
本文导出了p-Laplace算子本征值的演化方程。此外，我们还得到了以下主要结果。设（t）是闭流形上第n阶平均曲率流的非正规幂的解，λ1，p（t）是p-Laplace算子（p≥n）的第一特征值.在初始时刻= 0，若H> 0，则λ1，p（t）是非减的且沿[0，T）上第阶平均曲率流的非正规幂沿着几乎处处可微.最后，我们讨论了次平均曲率流的非正规幂下的一些有趣的单调量。
In this paper, we derive the evolution equation for the eigenvalues ofp-Laplace operator. Moreover, we show the following main results. Let (be a solution of the unnormalized powers of themth mean curvature flow on a closed manifold and λ1,p(t) be the first eigenvalue of the p-Laplace operator (p≥n). At the initial timet= 0, ifH> 0, andthen λ1,p(t) is nondecreasing and differentiable almost everywhere along the unnormalized powers of themth mean curvature flow on [0,T). At last, we discuss some interesting monotonic quantities under unnormalized powers of themth mean curvature flow.