Related papers: Heat kernel asymptotics for quaternionic contact m…

We consider the asymptotics of the discrete heat kernel on isoradial graphs for the case where the time and the edge lengths tend to zero simultaneously. Depending on the asymptotic ratio between time and edge lengths, we show that two…

We obtain an upper heat kernel bound for the Laplacian on metric graphs arising as one skeletons of certain polygonal tilings of the plane, which reflects the one dimensional as well as the two dimensional nature of these graphs.

In this paper we prove a short time asymptotic expansion of a hypoelliptic heat kernel on an Euclidean space and a compact manifold. We study the "cut locus" case, namely, the case where energy-minimizing paths which join the two points…

We give a short overview of the effective action approach in quantum field theory and quantum gravity and describe various methods for calculation of the asymptotic expansion of the heat kernel for second-order elliptic partial differential…

We estimate the heat kernel on a closed Riemannian manifold $M$, with $dim(M)\geq 3$, evolving under the Ricci-harmonic map flow and the result depends on some constants arising from a Sobolev imbedding theorem. In a special case, when the…

We establish small-time asymptotic expansions for heat kernels of hypoelliptic H\"ormander operators in a neighborhood of the diagonal, generalizing former results obtained in particular by M\'etivier and by Ben Arous. The coefficients of…

We consider the asymptotic expansion of the heat kernel of a generalized Laplacian for $t\to 0^+$ and characterize the coefficients $a_k$ of this expansion by a natural intertwining property. In particular we will give a closed formula for…

This paper is devoted to study the asymptotic expansion of the heat trace of the Dirichlet-to-Neumann map for the thermoelastic equation on a Riemannian manifold with doundary. By providing a method we can obtain all the coefficients of the…

We consider the basic heat operator on functions on a Riemannian foliation of a compact, Riemannian manifold, and we show that the trace of this operator has a particular short time asymptotic expansion. The coefficients in this expansion…

Upper and lower bounds on the heat kernel on complete Riemannian manifolds were obtained in a series of pioneering works due to Cheng-Li-Yau, Cheeger-Yau and Li-Yau. However, these estimates do not give a complete picture of the heat kernel…

In the sub-Riemannian manifolds, on the one hand, following Baudoin-Garofalo \cite{BaudoinGarofalo}, the upper bound for heat kernels associated to a class of locally subelliptic operators are given under the generalized curvature-dimension…

We study the spectral properties of the scalar Laplacian on a $n$-dimen\-sional warped product manifold $M=\Sigma\times_f N$ with a $(n-1)$-dimensional compact manifold $N$ without boundary, a one dimensional manifold $\Sigma$ without…

We consider a complete noncompact smooth Riemannian manifold $M$ with a weighted measure and the associated drifting Laplacian. We demonstrate that whenever the $q$-Bakry-\'Emery Ricci tensor on $M$ is bounded below, then we can obtain an…

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-…

This article shows that under locally uniformly integral bounds of the negative part of Ricci curvature the heat kernel admits a Gaussian upper bound for small times. This provides general assumptions on the geometry of a manifold such that…

We study the heat kernel for an operator of Laplace type with a $\delta$-function potential concentrated on a closed surface. We derive the general form of the small $t$ asymptotics and calculate explicitly several first heat kernel…

We establish in the present paper two sub-gradient estimates for the quaternionic contact (qc) heat equation on a compact qc manifold of dimension $4n+3$, provided some positivity conditions are satisfied. These are qc versions of the…

Let $X$ be an abstract orientable not necessarily compact CR manifold of dimension $2n+1$, $n\geq1$, and let $L^k$ be the $k$-th tensor power of a CR complex line bundle $L$ over $X$. Suppose that condition $Y(q)$ holds at each point of…

The heat kernels of Laplacians for spin 1/2, 1, 3/2 and 2 fields, and the asymptotic expansion of their traces are studied on manifolds with conical singularities. The exact mode-by-mode analysis is carried out for 2-dimensional domains and…

$H$-type foliations $(\mathbb{M},\mathcal{H},g_{\mathcal{H}})$ are studied in the framework of sub-Riemannian geometry with bracket generating distribution defined as the bundle transversal to the fibers. Equipping $\mathbb{M}$ with the…