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.

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.
Settore MAT/05 - Analisi Matematica
RCD spaces; Spectral analysis; Weyl’s law;
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/68927
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