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Exponential decay of Bergman kernels on complete Hermitian manifolds with Ricci curvature bounded from below
[article]
2019
arXiv
pre-print
Given a smooth positive measure μ on a complete Hermitian manifold with Ricci curvature bounded from below, we prove a pointwise Agmon-type bound for the corresponding Bergman kernel, under rather general conditions involving the coercivity of an associated complex Laplacian on (0,1)-forms. Thanks to an appropriate version of the Bochner--Kodaira--Nakano basic identity, we can give explicit geometric sufficient conditions for such coercivity to hold. Our results extend several known bounds in
arXiv:1804.07540v2
fatcat:yvveadzkhneijlzirzc6df52ei