Short-time behavior of the heat kernel and Weyl’s law on RCD ∗(K, N) spaces

Luigi Ambrosio; Shouhei Honda; David Tewodrose

doi:10.1007/s10455-017-9569-x

Short-time behavior of the heat kernel and Weyl’s law on RCD ^∗(K, N) spaces

Luigi Ambrosio, Shouhei Honda, David Tewodrose

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

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.

Original language	English
Pages (from-to)	97-119
Number of pages	23
Journal	Annals of Global Analysis and Geometry
Volume	53
Issue number	1
DOIs	https://doi.org/10.1007/s10455-017-9569-x
Publication status	Published - 2018 Jan 1

Keywords

RCD spaces
Spectral analysis
Weyl’s law

ASJC Scopus subject areas

Analysis
Political Science and International Relations
Geometry and Topology

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title = "Short-time behavior of the heat kernel and Weyl{\textquoteright}s law on RCD ∗(K, N) spaces",

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{\textquoteright}s law in the RCD setting.",

keywords = "RCD spaces, Spectral analysis, Weyl{\textquoteright}s law",

author = "Luigi Ambrosio and Shouhei Honda and David Tewodrose",

note = "Funding Information: Acknowledgements The first and third author acknowledge the support of the PRIN2015 MIUR Project “Calcolo delle Variazioni”. The second author acknowledges the support of the JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers, the Grant-in-Aid for Young Scientists (B) 16K17585 and the Scuola Normale Superiore for warm hospitality.",

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AU - Ambrosio, Luigi

AU - Honda, Shouhei

AU - Tewodrose, David

N1 - Funding Information: Acknowledgements The first and third author acknowledge the support of the PRIN2015 MIUR Project “Calcolo delle Variazioni”. The second author acknowledges the support of the JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers, the Grant-in-Aid for Young Scientists (B) 16K17585 and the Scuola Normale Superiore for warm hospitality.

PY - 2018/1/1

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N2 - 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.

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KW - RCD spaces

KW - Spectral analysis

KW - Weyl’s law

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