Related papers: Sharp estimates of the spherical heat kernel

We derive the asymptotic expansion of the heat kernel for a Laplace operator acting on deformed spheres. We calculate the coefficients of the heat kernel expansion on two- and three-dimensional deformed spheres as functions of deformation…

We consider a class of fourth order uniformly elliptic operators in planar Euclidean domains and study the associated heat kernel. For operators with $L^{\infty}$ coefficients we obtain Gaussian estimates with best constants, while for…

In this paper, we derive explicit sharp two-sided estimates for the Dirichlet heat kernels of a large class of symmetric (but not necessarily rotationally symmetric) L\'evy processes on half spaces for all $t>0$. These L\'evy processes may…

In his celebrated article, Aronson established Gaussian bounds for the fundamental solution to the Cauchy problem governed by a second order divergence form operator with uniformly elliptic coefficients. We extend Aronson's proof of upper…

We study the heat kernel of the sub-Laplacian L on the CR sphere S2n+1. An explicit and geometrically meaningful formula for the heat kernel is obtained. As a by-product we recover in a simple way the Green function of the conformal sub-…

In this paper we extend a gradient estimate of R. Hamilton for positive solutions to the heat equation on closed manifolds to bounded positive solutions on complete, non-compact manifolds with $Rc \geq -Kg$. We accomplish this extension via…

In this article, we establish Gaussian decay for the Box_b-heat kernel on polynomial models in C^2. Our technique attains the exponential decay via a partial Fourier transform. On the transform side, the problem becomes finding quantitative…

In this paper, we prove two-sided heat kernel estimates on what we call "book-like" graphs. These are graphs consisting of pieces that satisfy the parabolic Harnack inequality that are glued together in a sufficiently nice way over a…

We establish local asymptotic estimates of partial Bergman kernels on closed, $S^1$-symmetric K\"{a}hler manifolds. The main result concerns the scaling asymptotics of partial Bergman kernels at generic off-diagonal points in which they are…

There is a special relation between the spectrum and the {\it truncated} heat kernel of the Euclidean BTZ black hole with the Patterson-Selberg zeta function. Using an orbifold description of this relation we calculate the on-shell…

Under the assumption of positive multiplicity, we obtain basic estimates of the hypergeometric functions F\_\la and G\_\la of Heckman and Opdam, and sharp estimates of the particular functions F\_0 and G\_0. Next we prove the Paley-Wiener…

In the first part, we derive a sharp gradient estimate for the log of Dirichlet heat kernel and Poisson heat kernel on domains, and a sharpened local Li-Yau gradient estimate that matches the global one. In the second part, without explicit…

In this paper, we firstly establish weighted heat kernel comparison theorems for the weighted heat equation on complete manifolds with radial curvatures bounded, and then by mainly using this conclusion, we can obtain two eigenvalue…

We investigate when the fundamental solution of the Schr\"odinger equation $\partial_t=\Delta+V$ posseses sharp Gaussian bounds global in space and time. We give a characterization for $V\leq 0$ and a sufficient condition for general $V$.

In this paper, first we consider the uniform complex time heat kernel estimates of $e^{-z(-\Delta)^{\frac{\alpha}{2}}}$ for $\alpha>0, z\in \mathbb{C}^+$. When $\frac{\alpha}{2}$ is not an integer, generally the heat kernel doest not have…

We prove heat kernel estimates for the $\bar\partial$-Neumann Laplacian acting in spaces of differential forms over noncompact, strongly pseudoconvex complex manifolds with a Lie group symmetry and compact quotient. We also relate our…

In this paper, we prove sharp gradient estimates for positive solutions to the weighted heat equation on smooth metric measure spaces with compact boundary. As an application, we prove Liouville theorems for ancient solutions satisfying the…

This paper is concerned with the Poisson and heat equations on spaces of constant curvature. More explicitly we provide new methods for obtaining old and new explicit formulas for the Poisson and heat semigroups on the Euclidean, spherical…

We provide sharp two-sided estimates of the heat kernel of the Dirichlet fractional Laplacian on the half-line perturbed by the Hardy potential.

We consider smooth solutions to the biharmonic heat equation on Euclidean space for which the square of the Laplacian at time t is globally bounded from above by k/t for some k in R, for all t in [0,T]. We prove local, in space and time,…