First-order heat content asymptotics on \sf RCD(K,N) spaces

2022/12/12 by Caputo, Emanuele, Rossi, Tommaso · 1 citation
#35B40 #49J52 #53C23 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2212.06059

Abstract

In this paper, we prove first-order asymptotics on a bounded open set of the heat content when the ambient space is an \sf 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 by Cavalletti and Mondino.

Cited by

• Comparison estimates on nonsmooth spaces with integrable Ricci lower bounds via localization

Related

• Hypercontractivity of the heat flow on \sf RCD(0,N) spaces: sharpness and rigidities
• Heat Kernel Bounds on Metric Measure Spaces and Some Applications
• Short-time behavior of the heat kernel and Weyl's law on RCD^*(K, N)-spaces
• Distribution-Valued Ricci Bounds for Metric Measure Spaces, Singular Time Changes, and Gradient Estimates for Neumann Heat Flows
• Asymptotic behaviour of the heat equation in an exterior domain with general boundary conditions II. The case of bounded and of L^p data