Related papers: Heat kernel bounds, ancient $\kappa$ solutions and…

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…

Using time dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernels of some nonautonomous Kolmogorov operators with possibly unbounded drift and diffusion coefficients.

In this paper we provide a new (probabilistic) proof of a classical result in partial differential equations, viz. if $\phi$ is a tempered distribution, then the solution of the heat equation for the Laplacian, with initial condition…

We consider metric graphs with Kirchhoff boundary conditions. We study the intrinsic metric, volume doubling and a Poincar\'e inequality. This enables us to prove a parabolic Harnack inequality. The proof involves various techniques from…

In a 1991 paper by Buttig and Eichhorn, the existence and uniqueness of a differential forms heat kernel on open manifolds of bounded geometry was proven. In that paper, it was shown that the heat kernel obeyed certain properties, one of…

We derive an improved rigorous bound on the space and time averaged temperature $<T>$ of an infinite Prandtl number Boussinesq fluid contained between isothermal no-slip boundaries thermally driven by uniform internal heating. A novel…

Let $p:C\to R$ be a subharmonic, nonharmonic polynomial and $\tau\in R$ a parameter. Define $\bar Z_{\tau p} = \partial_{\bar z} + \tau p_{\bar z} = e^{-\tau p} p_{\bar z} e^{\tau p}$, a closed, densely defined operator on $L^2(C)$. If…

We study heat kernel estimates for symmetric pure jump processes on general metric measure spaces. Building on recent progress in the local setting due to S.~Eriksson-Bique, we develop a non-local version of the Whitney blending technique…

We provide general lower and upper bounds for Laplace Dirichlet heat kernel of convex $\mathcal C^{1,1}$ domains. The obtained estimates precisely describe the exponential behaviour of the kernels, which has been known only in a few special…

In the first part of this paper, we prove the global regularity, in an adequate parabolic Bessel-Potential space and then in the corresponding parabolic fractional Sobolev space, of the unique solution to following fractional heat equation…

In the present Letter we present an analytical and numerical solution of the self-consistent mode-coupling equations for the problem of heat conductivity in one-dimensional systems. Such a solution leads us to propose a different scenario…

We study reflected diffusion on uniform domains where the underlying space admits a symmetric diffusion that satisfies sub-Gaussian heat kernel estimates. A celebrated theorem of Jones (Acta Math. 1981) states that uniform domains in…

Given a domain $\Omega$ of a complete Riemannian manifold $\mathcal{M}$ and define $\mathcal{A}$ to be the Laplacian with Neumann boundary condition on $\Omega$. We prove that, under appropriate conditions, the corresponding heat kernel…

We develop the heat kernel method in the context of finite temperature quantum field theory. We compute the heat kernel expansion in the presence of general gauge and scalar fields which may be non Abelian and non stationary. The Polyakov…

In this paper, we prove logarithmic Sobolev inequalities and derive the Hamilton Harnack inequality for the heat semigroup of the Witten Laplacian on complete Riemannian manifolds equipped with $K$-super Perelman Ricci flow. We establish…

We apply the Davies method to prove that for any regular Dirichlet form on a metric measure space, an off-diagonal stable-type upper bound of the heat kernel is equivalent to the conjunction of the on-diagonal upper bound, a cutoff…

In our previous work we showed that for an ancient solution to the Ricci flow with nonnegative curvature operator, assuming bounded geometry on one time slice, bounded entropy implies noncollapsing on all scales. In this paper we prove the…

By studying the heat semigroup, we prove Li-Yau type estimates for bounded and positive solutions of the heat equation on graphs, under the assumption of the curvature-dimension inequality $CDE'(n,0)$, which can be consider as a notion of…

This paper presents a detailed analysis of the heat kernel on an $(\mathbb{N}\times\mathbb{N})$-parameter family of compact metric measure spaces, which do not satisfy the volume doubling property. In particular, uniform bounds of the heat…

We give a unified and optimized proof of the sharp bounds for the Jacobi heat kernel, which were obtained gradually in several papers in recent years. We lay particular emphasis on tracing and estimating all constants appearing throughout…