Gradient and Eigenvalue Estimates on the Canonical Bundle of Kähler Manifolds

被引：1
作者：
Zhiqin Lu
Qi S. Zhang
Meng Zhu
机构：
[1] University of California,Department of Mathematics
[2] University of California,Department of Mathematics
[3] East China Normal University,School of Mathematical Sciences and Shanghai Key Laboratory of PMMP
来源：
The Journal of Geometric Analysis | 2021年 / 31卷
关键词：
Eigenvalue; Gradient estimates; Kahler manifold;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We prove certain gradient and eigenvalue estimates, as well as the heat kernel estimates, for the Hodge Laplacian on (m, 0) forms, i.e., sections of the canonical bundle of Kähler manifolds, where m is the complex dimension of the manifold. Instead of the usual dependence on curvature tensor, our condition depends only on the Ricci curvature bound. The proof is based on a new Bochner type formula for the gradient of (m, 0) forms, which involves only the Ricci curvature and the gradient of the scalar curvature.
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页码：10304 / 10335
页数：31
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