Abstract

In this paper, we develop a universal way of obtaining Gaussian upper bounds of the heat kernel on Riemannian manifolds. By the word "Gaussian" we mean those estimates which contain a Gaussian exponential factor similar to one which enters the explicit formula for the heat kernel of the conventional Laplace operator in R...

Citations

210	Heat Kernels and Spectral Theory - Davies - 1989
133	Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds - Cheeger, Gromov, et al. - 1982
115	On the parabolic kernel of the Schrödinger operator - Li, Yau - 1986
88	Analysis and Geometry on Groups - Varopoulos, Saloff-Coste, et al. - 1992
74	Continuity of solutions of parabolic and elliptic equations - Nash - 1958
54	A new proof of Moser’s parabolic Harnack inequality using the old ideas of - Fabes, Stroock - 1986
46	Upper bounds for symmetric Markov transition functions - Carlen, Kusuoka, et al. - 1987
35	Non-negative solutions of linear parabolic equations - Aronson - 1968
29	On the upper estimate of the heat kernel on a complete Riemannian manifold - Cheng, Li, et al. - 1986
24	Inégalités isopérimétriques de Faber-Krahn et conséequences, Actes de la table ronde de géométrie différentielle (Luminy - Carron - 1992
23	Maximum Principle for Parabolic Inequalities and the Heat Flow - Dodziuk - 1983
16	Modified isoperimetric constants, and large time heat diffusion in Riemannian manifold - Chavel, Feldman - 1991
11	Two-sided estimates of the fundamental solutions of second-order parabolic equations and some applications of them, Uspekhi Mat. Nauk 39 - Porper, Èǐdel‘man - 1984
9	estimates for some functions of the Laplacian on noncompact symmetric spaces, Duke - Anker - 1992
7	Sharp Heat Kernel Bounds for some Laplace - Davies, Pang - 1989
6	Itération de Moser et estimation gaussienne du noyau de la chaleur - Coulhon - 1993
3	On uniform stabilization of the solution of the second mixed problem for a second order parabolic equation - Gushchin, Michailov, et al. - 1985
2	Upper Boundes for Heat Kernels of Some SecondOrder - Gaussian - 1988
2	bounds of derivatives of the heat kernel on an arbitrary complete manifold - Upper - 1995
2	kernel upper bounds on a complete non-compact manifold - Heat - 1994
2	maximum principle and its applications - Integral - 1994
1	Gaussian upper bounds for the heat kernel and for its derivatives on a Riemannian manifold - Grigor'yan - 1993
1	kernel on a manifold with a local Harnack inequality - Heat - 1994
1	On uniform stabilization of the solution of the second mixed problem for a second order parabolic equation - Michailov - 1985
1	Gaussian estimates for Markov chains and random walks on groups - Hebish - 1993
1	Stabilization of solutions of the third mixed problem for a second order parabolic equation in a non-cylindric domain - Ushakov - 1980
1	Hardy-Littlewood theory for semigoups - Varopoulos - 1985