Related papers: The asymptotic expansion of the heat kernel on a c…

We develop a new method for the calculation of the heat trace asymptotics of the Laplacian on symmetric spaces that is based on a representation of the heat semigroup in form of an average over the Lie group of isometries and obtain a…

It is well-known that the asymptotic expansion of the trace of the heat kernel for Laplace operators on smooth compact Riemmanian manifolds can be obtained through termwise integration of the asymptotic expansion of the on-diagonal heat…

We study the relationship between the geometry and the Laplace spectrum of a Riemannian orbifold O via its heat kernel; as in the manifold case, the time-zero asymptotic expansion of the heat kernel furnishes geometric information about O.…

We analyze the heat kernel associated to the Laplacian on a compact metric graph, with standard Kirchoff-Neumann vertex conditions. An explicit formula for the heat kernel as a sum over loops, developed by Roth and Kostrykin, Potthoff, and…

This is a mini-review of the heat kernel expansion for generalized Laplacians on various noncommutative spaces. Applications to the spectral action principle, renormalization of noncommutative theories and anomalies are also considered.

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 analyze the small-t asymptotic expansion of the trace of the heat kernel associated with a Laplace operator endowed with a spherically symmetric polynomially confining potential on the unbounded, d-dimensional Euclidean…

Let $G$ be a connected, real, semisimple Lie group with finite center, and $K$ a maximal compact subgroup of $G$. In this paper, we derive $K$-equivariant asymptotics for heat traces with remainder estimates on compact Riemannian manifolds…

Heat kernels are used in this paper to express the analytic index of projectively invariant Dirac type operators on G-covering spaces of compact manifolds, as elements in the K-theory of certain unconditional completions of the twisted…

We present a brief overview of several approaches for calculating the local asymptotic expansion of the heat kernel for Laplace-type operators. The different methods developed in the papers of both authors some time ago are described in…

We study the fifth term in the asymptotic expansion of the heat operator trace for a partial differential operator of Laplace type on a compact Riemannian manifold with Dirichlet or Neumann boundary conditions.

Let $\mathcal{M}$ be a smooth, closed and connected manifold of dimension $n\in\mathbb{N}$, endowed with a Riemannian metric $g$. Moreover, let $\mathcal{B}$ be an $(n+1)$-dimensional compact manifold with boundary equal to $\mathcal{M}$.…

We study a "div-grad type" sub-Laplacian with respect to a smooth measure and its associated heat semigroup on a compact equiregular sub-Riemannian manifold. We prove a short time asymptotic expansion of the heat trace up to any order. Our…

We study the heat kernel for a Laplace type partial differential operator acting on smooth sections of a complex vector bundle with the structure group $G\times U(1)$ over a Riemannian manifold $M$ without boundary. The total connection on…

We introduce a method of constructing a general Laakso space while calculating the spectrum and multiplicities of the Laplacian operator on it. Using this information, we found the leading term of the trace of the heat kernel of a Laakso…

A new algebraic approach for calculating the heat kernel for the Laplace operator on any Riemannian manifold with covariantly constant curvature is proposed. It is shown that the heat kernel operator can be obtained by an averaging over 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…

We establish the large-$N$ asymptotic expansion of the (central) trace of the heat kernel on any compact classical group $G_N\subset\mathrm{GL}_N(\mathbb{C})$, which extends a previous result known only for $\mathrm{U}(N)$ \cite{LM2}. It…

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 $c_1$…

The heat coefficients related to the Laplace-Beltrami operator defined on the hyperbolic compact manifold $H^3/\Ga$ are evaluated in the case in which the discrete group $\Ga$ contains elliptic and hyperbolic elements. It is shown that…