Related papers: Heat kernels on curved cones

The heat kernel on the symmetric space of positive definite Hermitian matrices is used to endow the spaces of Bergman metrics of degree k on a Riemann surface M with a family of probability measures depending on a choice of the background…

This paper studies by means of standard analytic tools the small time behavior of the heat content over a bounded Lebesgue measurable set of finite perimeter by working with the set covariance function and by imposing conditions on the heat…

Let M be a smooth closed (compact without boundary) Riemannian manifold of dimension n and P a q-dimensional smooth submanifold of M. U will denote the tubular neighborhood of P in M. Let E be a smooth vector bundle over M. Here we will…

We prove a conjecture of Bernstein that the superconvexity of the heat kernel on hyperbolic space holds in all dimensions and, hence, there is an analog of Huisken's monotonicity formula for mean curvature flow in hyperbolic space of all…

In this survey article, we discuss some recent progress on geometric analysis on manifold with ends. In the final section, we construct manifolds with ends with oscillating volume functions which may turn out to have a different heat kernel…

We obtain sharp estimates for heat kernels and Green's functions on complete noncompact Riemannian manifolds with Euclidean volume growth and nonnegative Ricci curvature. We will then apply these estimates to obtain sharp Moser-Trudinger…

We prove sharp estimates of the heat kernel associated with Fourier-Dini expansions on $(0,1)$ equipped with Lebesgue measure and the Neumann condition imposed on the right endpoint. Then we give several applications of this result…

Being motivated by physical applications (as the phi^4 model) we calculate the heat kernel coefficients for generalised Laplacians on the Moyal plane containing both left and right multiplications. We found both star-local and star-nonlocal…

The off-diagonal heat-kernel expansion of a Laplace operator including a general gauge-connection is computed on a compact manifold without boundary up to third order in the curvatures. These results are used to study the early-time…

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.

In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time…

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…

In this thesis we deal with spectral invariants for polygons and closed orbisurfaces of constant Gaussian curvature. In each case our method is to study the heat kernel and the asymptotic expansion of the heat trace. First, we investigate…

We show that, in odd dimensions, any real valued, bounded potential of compact support has at least one scattering resonance. For dimensions three and higher this was previously known only for sufficiently smooth potentials. The proof is…

We analyze the asymptotic behaviour of the heat kernel defined by a stochastically perturbed geodesic flow on the cotangent bundle of a Riemannian manifold for small time and small diffusion parameter. This extends WKB-type methods to a…

The aim of this paper is to construct (explicit) heat kernels for some hybrid evolution equations which arise in physics, conformal geometry and subelliptic PDEs. Hybrid means that the relevant partial differential operator appears in the…

We show a diffusive upper bound on the transition probability of a tagged particle in the symmetric simple exclusion process. The proof relies on optimal spectral gap estimates for the dynamics in finite volume, which are of independent…

Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector…

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 give a heat kernel proof of the algebraic index theorem for deformation quantization with separation of variables on a pseudo-Kahler manifold. We use normalizations of the canonical trace density of a star product and of the…