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On real Riemannian manifold , the heat kernel of the laplacian have an asymptotic expansion . But on complex manifold , i haven't seen a result like this , i.e. the heat kernel of the Kodaira Laplacian have an asymptotic expansion as the real case . Maybe I know so little , so I want to ask that Is there an asymptotic expansion of the heat kernel of the Kodaira laplacian ?

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  • $\begingroup$ Have you looked at "Holomorphic Morse Inequalities and Bergman Kernels" by Ma and Marinescu? I just saw the introduction, but it looks like it might have something similar to what you want. $\endgroup$
    – Kimball
    Jun 14, 2011 at 10:37

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