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Gradient and Eigenvalue Estimates on the Canonical Bundle of Kähler Manifolds

Authors :
Zhiqin Lu
Qi S. Zhang
Meng Zhu
Source :
The Journal of Geometric Analysis. 31:10304-10335
Publication Year :
2021
Publisher :
Springer Science and Business Media LLC, 2021.

Abstract

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 Kahler 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.

Details

ISSN :
1559002X and 10506926
Volume :
31
Database :
OpenAIRE
Journal :
The Journal of Geometric Analysis
Accession number :
edsair.doi...........6b850ccb0a52ad251ee8cdb8e333232b
Full Text :
https://doi.org/10.1007/s12220-021-00647-8