标题： 热含量的定性性质 显示英文标题

标题： Qualitative properties of the heat content

摘要： 我们得到了黎曼流形和欧几里得空间中区域的热含量关于不同初始温度条件的单调性和凸性结果。 我们引入了严格递减温度集的概念，并证明它是确保热含量单调的充分条件。 此外，在欧几里得空间中，我们构造了一个热含量非单调的区域和初始条件，以及一个热含量单调但非凸的区域和初始条件。 显示英文摘要

摘要： 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.