Qualitative properties of the heat content

Michiel van den Berg; Katie Gittins

doi:10.1112/blms.70091

Qualitative properties of the heat content

Michiel van den Berg^*
, Katie Gittins

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

Abstract

We obtain monotonicity and convexity results for the heat content of domains in Riemannian manifolds and in Euclidean space subject to various initial temperature conditions. We introduce the notion of a strictly decreasing temperature set, and show that it is a sufficient condition to ensure monotone heat content. In addition, in Euclidean space, we construct a domain and an initial condition for which the heat content is not monotone, as well as a domain and an initial condition for which the heat content is monotone but not convex.

Original language	English
Pages (from-to)	2239-2252
Number of pages	14
Journal	Bulletin of the London Mathematical Society
Volume	57
Issue number	8
Early online date	12 May 2025
DOIs	https://doi.org/10.1112/blms.70091
Publication status	Published - 1 Aug 2025

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© 2025 The Author(s). The Bulletin of the London Mathematical Society is copyright © London Mathematical Society.

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abstract = "We obtain monotonicity and convexity results for the heat content of domains in Riemannian manifolds and in Euclidean space subject to various initial temperature conditions. We introduce the notion of a strictly decreasing temperature set, and show that it is a sufficient condition to ensure monotone heat content. In addition, in Euclidean space, we construct a domain and an initial condition for which the heat content is not monotone, as well as a domain and an initial condition for which the heat content is monotone but not convex. ",

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AB - We obtain monotonicity and convexity results for the heat content of domains in Riemannian manifolds and in Euclidean space subject to various initial temperature conditions. We introduce the notion of a strictly decreasing temperature set, and show that it is a sufficient condition to ensure monotone heat content. In addition, in Euclidean space, we construct a domain and an initial condition for which the heat content is not monotone, as well as a domain and an initial condition for which the heat content is monotone but not convex.

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DO - 10.1112/blms.70091

M3 - Article (Academic Journal)

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JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

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Qualitative properties of the heat content

Abstract

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