arXiv research

Quantitative Sobolev extensions lead to Neumann heat kernel bounds.

We study new heat kernel estimates for the Neumann heat kernel on a compact manifold with positive Ricci curvature and convex boundary. As a consequence, we obtain new lower bounds for the Neumann eigenvalues which are consistent with Weyl's asymptotics.

The paper compares heat kernels on manifolds with Robin boundary conditions.

Constructs index for elliptic operators using rapidly decaying kernels.

Extends Onsager's conjecture to Besov spaces on manifolds with boundary.

We consider the Hodge Laplacian on manifolds with incomplete edge singularities, with infinite dimensional von Neumann spaces and intricate elliptic boundary value theory. We single out a class of its algebraic self-adjoint extensions. Our microlocal heat kernel construction for algebraic boundary conditions is guided …

Study reveals how to determine area and curvature from fluid flow resonances.

On a large class of Riemannian manifolds with boundary, some dimension-free Harnack inequalities for the Neumann semigroup is proved to be equivalent to the convexity of the boundary and a curvature condition. In particular, for $p_t(x,y)$ the Neumann heat kernel w.r.t. a volume type measure $μ$ and for $K$ a constant,…

Study on heat trace expansion for thermoelastic Dirichlet-to-Neumann map.

New method reveals corners of drum shapes.

The paper improves eigenvalue estimates for manifolds with Ricci curvature conditions.

Study heat flow on collapsing K3 surfaces, handling conic singularities.

Study heat profiles and eigenfunctions using Brownian motion.

Sharp estimates for heat flow on nonconvex domains.

D.Freed has formulated and proved an index theorem on odd dimensional spin manifolds with boundary. The proof is based on analysis by Calderon and Seeley. In this note we are going to give a proof of this theorem using the heat kernels methods for boundary conditions of Dirichlet and Von Neumann type. Moreover we consi…

New approach to heat flow for half-harmonic maps, related to minimal surfaces.

New algorithms for clustering and dimension reduction using relative von Neumann entropy.

We give a short proof of a strong version of the short time asymptotic expansion of heat kernels associated to Laplace type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the difference of the approximate heat kernel and the true heat kernel. We use this…

The heat kernel for the Cauchy-Riemann subLaplacian on S(2n+1) is derived in a manner which is completely analogous to the classical derivation of elliptic heat kernels. This suggests that the classical hamiltonian construction of elliptic heat kernels, with appropriate modifications, does yield heat kernels for subell…

The paper studies heat kernel asymptotics and proves Morse inequalities.

Paper generalizes kernel mean embedding to von Neumann-algebra-valued measures.

Formulae connect heat kernels on glued manifolds.

New heat trace coefficients reveal curvature effects in polygonal domains.

We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We show explicitly that the obtaine…

Proves upper bounds for heat kernels evolving on manifolds.

In this paper, we first give a direct proof for two recurrence relations of the heat kernels for hyperbolic spaces in \cite{DM}. Then, by similar computation, we give two similar recurrence relations of the heat kernels for spheres. Finally, as an application, we compute the diagonal of heat kernels for odd dimensional…

We investigate the problem of calculating the Fredholm index of a geometric Dirac operator subject to local (e.g. Dirichlet and Neumann) and non-local (APS) boundary conditions posed on the strata of a manifold with corners. The boundary strata of the manifold with corners can intersect in higher codimension. To calcul…

From the uniformization theorem, we know that every Riemann surface has a simply-connected covering space. Moreover, there are only three simply-connected Riemann surfaces: the sphere, the Euclidean plane, and the hyperbolic plane. In this paper, we collect the known heat kernels, or Green's functions, for these three …

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 which was a relationship between the derivative of heat kernel of different degree…

Heat kernel estimates on manifolds with mixed boundary conditions.

Proves heat kernel superconvexity in hyperbolic space.

Derives properties of heat kernel for Rumin complex on Heisenberg groups.

Proposes learning manifold implicitly via heat kernel.

The paper studies local heat kernel properties on smooth manifolds.

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 estimate on Laplacian form of the heat kernel on complete manifolds with nonnegative R…

The paper studies heat kernel asymptotics for Kohn Laplacians on CR manifolds.

Heat kernel resurgent structure from Picard-Lefschetz theory

The paper develops heat kernel comparison theorems and applies them to spectral geometry.

Proves metric spaces with Euclidean heat kernel are isometric to Euclidean space.

In this paper, we study the large time behavior of the heat kernel on complete Riemannian manifolds with nonnegative Ricci curvature, which was studied by P. Li with additional maximum volume growth assumption. Following Y. Ding's original strategy, by blowing down the metric, using Cheeger and Colding's theory about l…

We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We argue that the obtained formal s…

Estimates heat kernel gradients on fractal-like cable systems.

The study examines heat kernel bounds on Riemannian manifolds with an end.

Sharp Gaussian bounds derived for Schrödinger kernel on Ricci solitons.

The geometry of the quaternionic anti-de Sitter fibration is studied in details. As a consequence, we obtain formulas for the horizontal Laplacian and subelliptic heat kernel of the fibration. The heat kernel formula is explicit enough to derive small time asymptotics. Related twistor spaces and corresponding heat kern…

New heat kernel bounds on manifolds with non-negative Ricci curvature.

Researchers derived heat kernel expansions for non-compact spaces using Witten deformation.

Extends heat kernel estimates for super Ricci flow.