arXiv research

Study asymptotics of Poisson kernel and Green's functions for fractional conformal Laplacian.

Sharp heat kernel and Green's function estimates on Euclidean volume growth manifolds.

The paper proves existence and growth estimates for inverse mean curvature flow and related $p$-Laplacian Green kernel decay.

Study rigidity by logarithmic capacity and related functions.

We obtain an off-diagonal upper bound for Green and heat kernel of Laplace type operator on symmetric spaces.

This paper consists of two parts. In the first part we show that in odd dimension, as well as in even dimension below the critical weight (i.e. half the dimension), the logarithmic singularities of Schwartz kernels and Green kernels of conformal invariant pseudodifferential operators are linear combinations of Weyl con…

The paper discusses methods to compute Green's function on algebraic surfaces using Schottky uniformization.

Unified framework for constructing kernels for transport equations and Koopman eigenfunctions.

Sharp Gaussian bounds derived for Schrödinger kernel on Ricci solitons.

Simple proof that stable minimal hypersurfaces in R^4 are hyperplanes.

This paper is being replaced by another of the author's that contains a brief summary of the problem of positivity of Green's functions, heat kernels, and principal eigenvalues of higher-order elliptic differential operators.

A regression algorithm uses Green's function and covariance matrix for predictive distributions.

This paper introduces a probability density estimator based on Green's function identities. A density model is constructed under the sole assumption that the probability density is differentiable. The method is implemented as a binary likelihood estimator for classification purposes, so issues such as mis-modeling and …

Geometric theory connects machine learning classifiers to differential geometry.

We construct radial fundamental solutions for the differential form Laplacian on negatively curved symmetric spaces. At least one of these Green's functions also yields a Biot-Savart Opearator, i.e. a right inverse of the exterior differential on closed forms with image in the kernel of the codifferential. Any Biot-Sav…

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 this article we study point configurations minimizing the discrete energy on a compact Riemannian manifold, where the energy kernel is taken to be the Green's function for the Laplacian. We show that every point in a minimizing configuration lies inside an open set called harmonic ball where no other point can enter…

We study the sub-Laplacian of the $15$-dimensional unit sphere which is obtained by lifting with respect to the Hopf fibration the Laplacian of the octonionic projective space. We obtain in particular explicit formulas for its heat kernel and deduce an expression for the Green function of a related sub-Laplacian. As a …

Using Roelcke formula for the Green function, we explicitly construct a basis in the kernel of the adjoint Laplacian on a compact polyhedral surface $X$ and compute the $S$-matrix of $X$ at the zero value of the spectral parameter. We apply these results to study various self-adjoint extensions of a symmetric Laplacian…

We study the heat kernel of the sub-Laplacian L on the CR sphere S2n+1. An explicit and geometrically meaningful formula for the heat kernel is obtained. As a by-product we recover in a simple way the Green function of the conformal sub- Laplacian -L + n2 that was obtained by Geller [12], and also get an explicit formu…

We consider second-order elliptic partial differential operators acting on sections of vector bundles over a compact Riemannian manifold without boundary, working without the assumption of Laplace-like principal part $-\N^μ\N_μ$. Our objective is to obtain information on the asymptotic expansions of the corresponding r…

The main goal of this work is to study the sub-Laplacian of the unit sphere which is obtained by lifting with respect to the Hopf fibration the Laplacian of the quaternionic projective space. We obtain in particular explicit formulas for its heat kernel and deduce an expression for the Green function of the conformal s…

We study the non-asymptotic behavior of a Coulomb gas on a compact Riemannian manifold. This gas is a symmetric n-particle Gibbs measure associated to the two-body interaction energy given by the Green function. We encode such a particle system by using an empirical measure. Our main result is a concentration inequalit…

Deformations of compact Riemann surfaces are considered using a Čech cohomology sliding overlaps approach. Cocycles are calculated for conformal cutting and regluing deformations at zeros of Abelian differentials. A second order deformation expansion is presented for the Riemann period matrix. A complete deformation ex…

Study of integral flows on Riemannian manifolds with focus on blow-up profiles and concentration-compactness.

Estimates Poisson kernel on negatively curved Hadamard manifolds.

In this paper we study Clifford and harmonic analysis on some conformal flat spin manifolds. In particular we treat manifolds that can be parametrized by $U / Γ$ where $U$ is a simply connected subdomain of either $S^{n}$ or $R^{n}$ and $Γ$ is a Kleinian group acting discontinuously on $U$. Examples of such manifolds t…

We develop heat kernel and Green's function estimates for manifolds with positive bottom spectrum. The results are then used to establish existence and sharp estimates of the solution to the Poisson equation on such manifolds with Ricci curvature bounded below. As an application, we show that the curvature of a steady …

We derive a Harnack inequality for positive solutions of the $f$-heat equation and Gaussian upper and lower bounds for the $f$-heat kernel on complete smooth metric measure spaces $(M, g, e^{-f}dv)$ with Bakry-Émery Ricci curvature bounded below. The lower bound is sharp. The main argument is the De Giorgi-Nash-Moser t…

Green startups in Italy survive longer than non-green ones.

Formula for Hadamard coefficients from Green's operators on spacetimes.

We study the horizontal Laplacian $Δ^H$ associated to the Hopf fibration $S^3\to S^2$ with arbitrary Chern number $k$. We use representation theory to calculate the spectrum, describe the heat kernel and obtain the complete heat trace asymptotics of $Δ^H$. We express the Green functions for associated Poisson semigroup…

Green stocks show less factor exposure heterogeneity compared to brown stocks.

Without using the $L^2$ extension theorem, we provide a new proof of the equality part in Suita's conjecture, which states that for any open Riemann surface admitting a Green's function, the Bergman kernel and the logarithmic capacity coincide at one point if and only if the surface is biholomorphic to a disc possibly …

Model shows government incentives boost green bond investment.

Green functions on stationary varifolds established with inequalities and convergence results.

Both analytic and geometric forms of an optimal monotone principle for $L^p$-integral of the Green function of a simply-connected planar domain $Ω$ with rectifiable simple curve as boundary are established through a sharp one-dimensional power integral estimate of Riemann-Stieltjes type and the Huber analytic and geome…

The paper derives expansions for Green's operators and resolvents using Hadamard methods.

The paper provides formulas for Hadamard coefficients using Green's operators.

A new approach for green investing in Indian markets considers environmental factors.

Study on $p$-Green functions on specific manifolds, proving monotonicity.

Margin trading and short selling boost green tech innovation in China.

On compact surfaces, a Green-Wasserstein inequality cannot be improved without the sqrt(log n) factor.

We study several quantities associated to the Green's function of a multiply connected domain in the complex plane. Among them are some intrinsic properties such as geodesics, curvature, and $L^2$-cohomology of the capacity metric and critical points of the Green's function. The principal idea used is an affine scaling…

In this paper, we define the Green function for the Dirac operator under two local boundary conditions: the condition associated with a chirality operator (also called the chiral bag boundary condition) and the $\MIT$ bag boundary condition. Then we give some applications of these constructions for each Green function.…

The paper analyzes risk spillovers between AI ETFs, AI tokens, and green markets.

Green functions for GJMS operators on spheres derived, linking geometry and rigidity.

Survey on rigidity and almost rigidity of Green functions in non-negative Ricci curvature spaces.