Talk by Tommaso Rossi
On June 28th, 2023, Tommaso Rossi (Universität Bonn) gave a talk about "First-order heat content asymptotics on RCD(K,N) spaces" as part of the research seminar Analysis of the FernUniversität in Hagen. This lecture is partially supported by the COST action Mathematical models for interacting dynamics on networks.
Abstract
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We study the small-time asymptotics of the heat content associated with a bounded open set when the ambient space is an RCD(K,N) metric measure space. By adapting a technique due to Savo, we establish the existence of a first-order asymptotic expansion, under a regularity condition for the boundary of the domain that we call measured interior geodesic condition. We carefully study such a condition, relating it to the properties of the disintegration associated with the signed distance function from the boundary. This is a joint work with Emanuele Caputo.
