First-order heat content asymptotics on RCD(K,N) spaces
Caputo, E., & Rossi, T. (2024). First-order heat content asymptotics on RCD(K,N) spaces. Nonlinear Analysis: Theory, Methods and Applications, 238, Article 113385. https://doi.org/10.1016/j.na.2023.113385
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Nonlinear Analysis: Theory, Methods and ApplicationsDate
2024Copyright
©2023 The Author(s). Published by Elsevier Ltd.
In this paper, we prove first-order asymptotics on a bounded open set of the heat content when the ambient space is an RCD(K, N) space, under a regularity condition for the boundary that we call measured interior geodesic condition of size ϵ. We carefully study such a condition, relating it to the properties of the disintegration of the signed distance function from ∂Ω studied in Cavalletti and Mondino (2020).
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Academy Project, AoFAdditional information about funding
E.C. acknowledges support from the Academy of Finland Grant No. 314789 and the kind hospitality of University of Bonn. T.R. acknowledges support from the Deutsche Forschungsgemeinschaft, Germany (DFG, German Research Foundation) through the collaborative research centre “The mathematics of emerging effects” (CRC 1060, Project-ID 211504053) and the kind hospitality of University of Jyväskylä .License
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