Gradient and Eigenvalue Estimates on the Canonical Bundle of Kähler Manifolds
| Autor: | Zhiqin Lu, Qi S. Zhang, Meng Zhu |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
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 |
| Zdroj: | The Journal of Geometric Analysis. 31:10304-10335 |
| ISSN: | 1559-002X 1050-6926 |
| DOI: | 10.1007/s12220-021-00647-8 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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