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Heat kernel on analytic subvariety. (English) Zbl 1436.32120

Summary: In this paper, the author extends Peter Li and Tian Gang’s results on the heat kernel from projective varieties to analytic varieties. The author gets an upper bound of the heat kernel on analytic varieties and proves several properties. Moreover, the results are extended to vector bundles. The author also gets an upper bound of the heat operators of some Schrödinger type operators on vector bundles. As a corollary, an upper bound of the trace of the heat operators is obtained.

MSC:

32W30 Heat kernels in several complex variables
53C40 Global submanifolds
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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