On the first eigenvalue of the Witten-Laplacian and the diameter of compact shrinking solitons
On the first eigenvalue of the Witten-Laplacian and the diameter of compact shrinking solitons
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关于维滕-拉普拉斯算子的第一特征值和紧缩孤子的直径
DOI：
10.1007/s10455-012-9358-5
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发表时间：
2013-08-01
影响因子：
0.7
通讯作者：
Li, Xiang-Dong
中科院分区：
文献类型：
--
作者：
Futaki, Akito;Li, Haizhong;Li, Xiang-Dong
证明了紧黎曼流形上Witten-Laplace算子的第一个非零本征值的下界估计。作为应用，我们得到了紧致梯度收缩Ricci孤子直径的下界估计。我们的结果改进了第一作者和Sano(即将出现的亚洲J数学)以及Andrews和Ni(即将出现的Comm偏微分方程组)所得到的一些估计。此外，我们将直径估计推广到平均曲率流的紧自相似收缩算子。
We prove a lower bound estimate for the first non-zero eigenvalue of the Witten-Laplacian on compact Riemannian manifolds. As an application, we derive a lower bound estimate for the diameter of compact gradient shrinking Ricci solitons. Our results improve some previous estimates which were obtained by the first author and Sano (Asian J Math, to appear), and by Andrews and Ni (Comm Partial Differential Equ, to appear). Moreover, we extend the diameter estimate to compact self-similar shrinkers of mean curvature flow.