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