热含量的定性性质

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-05-12 DOI:10.1112/blms.70091

Michiel van den Berg, Katie Gittins

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引用次数: 0

摘要

得到黎曼流形和欧几里德空间中不同初始温度条件下区域热含量的单调性和凸性结果。我们引入了严格递减温度集的概念，并证明了它是保证热含量单调的充分条件。此外，在欧几里得空间中，构造了热容量非单调的域和初始条件，以及热容量单调但不凸的域和初始条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Qualitative properties of the heat content

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Qualitative properties of the heat content

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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