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Article overview
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Gradient and Eigenvalue Estimates on the canonical bundle of Kähler manifolds | | Zhiqin Lu
; Qi S. Zhang
; Meng Zhu
; | | Date: |
30 Aug 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 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. | | Source: | arXiv, 2008.13282 | | Services: | Forum | Review | PDF | Favorites | |
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