In this paper, we prove pointwise convergence of heat kernels for mGH-convergent sequences of RCD∗(K,N)-spaces. We obtain as a corollary results on the short-time behavior of the heat kernel in RCD∗(K,N)-spaces. We use then these results to initiate the study of Weyl’s law in the RCD setting.
Short-time behavior of the heat kernel and Weyl’s law on RCD^*(K,N) spaces spaces
Ambrosio, Luigi
;TEWODROSE, David
2018
Abstract
In this paper, we prove pointwise convergence of heat kernels for mGH-convergent sequences of RCD∗(K,N)-spaces. We obtain as a corollary results on the short-time behavior of the heat kernel in RCD∗(K,N)-spaces. We use then these results to initiate the study of Weyl’s law in the RCD setting.File in questo prodotto:
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Ann_Glob_Anal_Geom_2018.pdf
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Ambrosio_Honda_Tewodrose_12.01.2017.pdf
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