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Gradient and Eigenvalue Estimates on the canonical bundle of K\'ahler manifolds
- Publication Year :
- 2020
-
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 K\"ahler 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.
- Subjects :
- Mathematics - Differential Geometry
58A10, 58J35, 58J50
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2008.13282
- Document Type :
- Working Paper