Heat Kernel on Analytic Subvariety

Abstract

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 Schröndinger type operators on vector bundles. As a corollary, an upper bound of the trace of the heat operators is obtained.

Keywords

Heat kernel / Analytic subvariety / Schröndinger operator

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