The First Eigenvalue of Witten-Laplacian on Manifolds with Time-Dependent Metrics

被引：0
作者：
Jian-hong Wang
机构：
[1] Shanghai Lixin University of Accounting and Finance,School of Statistics and Mathematics
来源：
Bulletin of the Iranian Mathematical Society | 2022年 / 48卷
关键词：
Ricci flow; Witten-Laplacian; First eigenvalue; Monotonicity; Differentiability; 58C40; 53C44;
D O I：
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摘要：
The main purpose of this paper is to discuss the monotonicity and differentiability for the first eigenvalue of Witten-Laplacian on closed metric measure spaces with time-dependent metrics. We show that the first eigenvalue of Witten-Laplacian is monotonous and differentiable almost everywhere along Ricci flow or modified Ricci flow with different potentials. We conclude some properties on gradient Ricci solitons and Ricci breathers as applications. Meanwhile, some monotonic quantities about the first eigenvalue of Witten-Laplacian are observed. Lastly, we derive a Witten-eigenvalue comparison theorem on closed surfaces. These conclusions are natural extension of some known results for Laplace–Beltrami operator under the Ricci flow.
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页码：2621 / 2641
页数：20
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