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Gradient and Eigenvalue Estimates on the Canonical Bundle of Kähler Manifolds
- 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.
- Subjects :
- Riemann curvature tensor
Pure mathematics
010102 general mathematics
Complex dimension
01 natural sciences
Manifold
Canonical bundle
symbols.namesake
Differential geometry
0103 physical sciences
symbols
Mathematics::Differential Geometry
010307 mathematical physics
Geometry and Topology
0101 mathematics
Mathematics::Symplectic Geometry
Laplace operator
Ricci curvature
Scalar curvature
Mathematics
Subjects
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