Heat Kernel on Analytic Subvariety


Luobin FANG.Heat Kernel on Analytic Subvariety[J].Chinese Annals of Mathematics B,2020,41(2):227~240
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Luobin FANG;
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 Schr\"ondinger type operators on vector bundles. As a corollary, an upper bound of the trace of the heat operators is obtained.


Heat kernel, Analytic subvariety, Schr"ondinger operator


53C21, 53C55 32W30
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