Abstract
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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