Pointwise monotonicity of heat kernels.

IF 1.4 3区数学 Q1 MATHEMATICS

Revista Matematica Complutense Pub Date : 2023-01-01 DOI:10.1007/s13163-021-00417-8

Diego Alonso-Orán, Fernando Chamizo, Ángel D Martínez, Albert Mas

引用次数: 6

Abstract

In this paper we present an elementary proof of a pointwise radial monotonicity property of heat kernels that is shared by the Euclidean spaces, spheres and hyperbolic spaces. The main result was discovered by Cheeger and Yau in 1981 and rediscovered in special cases during the last few years. It deals with the monotonicity of the heat kernel from special points on revolution hypersurfaces. Our proof hinges on a non straightforward but elementary application of the parabolic maximum principle. As a consequence of the monotonicity property, we derive new inequalities involving classical special functions.

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热核的逐点单调性。

本文给出了欧几里德空间、球空间和双曲空间所共有的热核的一个点向径向单调性的初等证明。主要结果是由Cheeger和Yau在1981年发现的，并在最近几年在一些特殊情况下被重新发现。讨论了旋转超曲面上特殊点的热核单调性问题。我们的证明取决于抛物线极大值原理的一个不直接但很基本的应用。根据单调性，我们得到了涉及经典特殊函数的新的不等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Revista Matematica Complutense 数学-数学

CiteScore

2.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Revista Matemática Complutense is an international research journal supported by the School of Mathematics at Complutense University in Madrid. It publishes high quality research and survey articles across pure and applied mathematics. Fields of interests include: analysis, differential equations and applications, geometry, topology, algebra, statistics, computer sciences and astronomy. This broad interest is reflected in our interdisciplinary editorial board which is comprised of over 30 internationally esteemed researchers in diverse areas. The Editorial Board of Revista Matemática Complutense organizes the “Santaló Lecture”, a yearly event where a distinguished mathematician is invited to present a lecture at Complutense University and contribute to the journal. Past lecturers include: Charles T.C. Wall, Jack K. Hale, Hans Triebel, Marcelo Viana, Narayanswamy Balakrishnan, Nigel Kalton, Alfio Quarteroni, David E. Edmunds, Giuseppe Buttazzo, Juan L. Vázquez, Eduard Feireisl, Nigel Hitchin, Lajos Horváth, Hélène Esnault, Luigi Ambrosio, Ignacio Cirac and Bernd Sturmfels. The Santaló Lecturer for 2019 will be Noel Cressie from National Institute for Applied Statistics Research Australia (NIASRA), University of Wollongong.