Related papers: Heat kernel transform for nilmanifolds associated …

We give a short proof of a strong version of the short time asymptotic expansion of heat kernels associated to Laplace type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the…

From the uniformization theorem, we know that every Riemann surface has a simply-connected covering space. Moreover, there are only three simply-connected Riemann surfaces: the sphere, the Euclidean plane, and the hyperbolic plane. In this…

Let $X$ be a compact hyperbolic Riemann surface equipped with the Poincar\'e metric. For any integer $k\geq 2$, we investigate the Bergman kernel associated to the holomorphic Hermitian line bundle $\Omega^{\otimes k}_X$, where $\O$ is the…

In this note we establish the large time non-negativity of the heat kernel for a class of elliptic differential operators on closed, Riemannian manifolds, and apply this result to a problem from conformal differential geometry.

Let $\Omega$ be an open set in a complete, smooth, non-compact, $m$-dimensional Riemannian manifold $M$ without boundary, where $M$ satisfies a two-sided Li-Yau gaussian heat kernel bound. It is shown that if $\Omega$ has infinite measure,…

The aim of the present paper is three folds. For a reproducing kernel Hilbert space $\mathcal{A}$ (R.K.H.S) and a $\sigma-$finite measure space $(M_{1},d\mu_{1})$ for which the corresponding $L^{2}-$space is a separable Hilbert space, we…

In this paper we give Hamilton's Laplacian estimates for the heat equation on complete noncompact manifolds with nonnegative Ricci curvature. As an application, combining Li-Yau's lower and upper bounds of the heat kernel, we give an…

We show that, on a complete, connected and non-compact Riemannian manifold of non-negative Ricci curvature, the solution to the heat equation with $L^{1}$ initial data behaves asymptotically as the mass times the heat kernel. In contrast to…

We prove a formula for the Bergman kernel of polarized complex hyperbolic manifolds. The formula expresses the Bergman kernel as a sum over the geodesic loops in the manifold. As an application, we prove a result about the maximum and…

It is shown that the heat operator in the Hall coherent state transform for a compact Lie group $K$ is related with a Hermitian connection associated to a natural one-parameter family of complex structures on $T^*K$. The unitary parallel…

In a previous paper we have presented a general formalism for computing Feynman diagrams for scalar fields in curved spacetime at any loop order using heat kernel methods. The main technique used is the expansion of the fully off-diagonal…

In this article, we consider the radial Dunkl geometric case $k=1$ corresponding to flat Riemannian symmetric spaces in the complex case and we prove exact estimates for the positive valued Dunkl kernel and for the radial heat kernel. Dans…

Let $\Gamma\subset \mathrm{SU}((2,1),\mathbb{C})$ be a torsion-free cocompact subgroup. Let $\mathbb{B}^{2}$ denote the $2$-dimensional complex ball endowed with the hyperbolic metric $\mu_{\mathrm{hyp}}$, and let…

Classical and non classical Besov and Triebel-Lizorkin spaces with complete range of indices are developed in the general setting of Dirichlet space with a doubling measure and local scale-invariant Poincar\'e inequality. This leads to Heat…

The conformal powers of the Laplacian of a Riemannian metric which are known as the GJMS-operators admit a combinatorial description in terms of the Taylor coefficients of a natural second-order one-parameter family $\H(r;g)$ of…

In this article, we consider flat and curved Riemannian symmetric spaces in the complex case and we study their basic integral kernels, in potential and spherical analysis: heat, Newton, Poisson kernels and spherical functions, i.e. the…

We obtain the asymptotic expansion of the solutions of some anisotropic heat equations when the initial data belong to polynomially weighted Lp-spaces. We mainly address two model examples. In the first one, the diffusivity is of order two…

The heat kernel associated with an elliptic second-order partial differential operator of Laplace type acting on smooth sections of a vector bundle over a Riemannian manifold, is studied. A general manifestly covariant method for…

In this paper, we study the heat kernel associated to the intrinsic sublaplacian on a quaternionic contact manifold considered as a subriemannian manifold. More precisely, we explicitly compute the first two coefficients $c_0$ and $c_1$…

We provide a study of the Riesz transforms on stratified nilpotent Lie groups, and obtain a certain version of the pointwise lower bound of the Riesz transform kernel. Then we establish the characterisation of the BMO space on stratified…