Related papers: On monotonicity of heat kernels: a new example and…
An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified…
We suggest a method of reduction of mixed absolute and relative boundary conditions to pure ones. The case of rank two tensor is studied in detail. For four-dimensional disk the corresponding heat kernel is expressed in terms of scalar heat…
We generalize the well-known "12" and "24" Theorems for reflexive polytopes of dimension 2 and 3 to any smooth reflexive polytope. Our methods apply to a wider category of objects, here called reflexive GKM graphs, that are associated with…
We consider the geometric inverse problem of determining a closed Riemannian manifold from measurements of the heat kernel in an open subset of the manifold. In this paper we analyze the stability of this problem in the class of…
Bayesian Optimization (BO) has the potential to solve various combinatorial tasks, ranging from materials science to neural architecture search. However, BO requires specialized kernels to effectively model combinatorial domains. Recent…
We prove that a metric measure space equipped with a Dirichlet form admitting an Euclidean heat kernel is necessarily isometric to the Euclidean space. This helps us providing an alternative proof of Colding's celebrated almost rigidity…
Manifolds with fibered cusps are a class of complete noncompact Riemannian manifolds including all locally symmetric spaces of rank one. We study the spectrum of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold…
This article shows that if the negative part of Ricci curvature lies in the Kato class, the heat kernel satisfies a Li-Yau type estimate. Additionally, using the resulting heat kernel bound, we show that the obtained heat kernel estimate…
We study the statistical monotonicity of the scalar curvature for the alpha-geometries on the simplex of probability vectors. From the results obtained and from numerical data we are led to some conjectures about quantum alpha-geometries…
In this paper we suggest new effective criteria for the density property. This enables us to give a trivial proof of the original Anders\'en-Lempert result and to establish (almost free of charge) the algebraic density property for all…
Let $\Omega_0$ be a polygon in $\RR^2$, or more generally a compact surface with piecewise smooth boundary and corners. Suppose that $\Omega_\e$ is a family of surfaces with $\calC^\infty$ boundary which converges to $\Omega_0$ smoothly…
It is shown that many results, previously believed to be properties of the Lichnerowicz Ricci curvature, hold for the Ricci curvature of all Gauduchon connections. We prove the existence of $t$--Gauduchon Ricci-flat metrics on the…
Following Osipov and Hiller, a generalized heat kernel expansion is considered for the effective action of bosonic operators. In this generalization, the standard heat kernel expansion, which counts inverse powers of a c-number mass…
We investigate the asymptotic behavior of solutions to a semilinear heat equation with homogeneous Neumann boundary conditions. It was recently shown that the nontrivial kernel of the linear part leads to the coexistence of fast solutions…
By means of a space-time Wasserstein control, we show the monotonicity of the W-entropy functional in time along heat flows on possibly singular metric measure spaces with non-negative Ricci curvature and a finite upper bound of dimension…
The asymptotic behavior of the heat kernel of a Riemannian manifold gives rise to the classical concepts of parabolicity, stochastic completeness (or conservative property) and Feller property (or $C^{0}$-diffusion property). Both…
Let $G$ be a simple, finite graph and let $p_t(x,y)$ denote the heat kernel on $G$. The purpose of this short note is to show that for $t \rightarrow 0^+$ $$ p_t(x,y) = \# \left\{\mbox{paths of…
In this paper we establish the existence and uniqueness of heat kernels to a large class of time-inhomogenous non-symmetric nonlocal operators with Dini's continuous kernels. Moreover, quantitative estimates including two-sided estimates,…
In this paper, we derive general monotone quantities and geometric inequalities associated with $p$-capacitary functions in asymptotically flat $3$-manifolds with simple topology and nonnegative scalar curvature. The inequalities become…
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…