arXiv research

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…

We lay the foundations for a theory of divergence-measure fields in noncommutative stratified nilpotent Lie groups. Such vector fields form a new family of function spaces, which generalize in a sense the $BV$ fields. They provide the most general setting to establish Gauss-Green formulas for vector fields of low regul…

Study rigidity by logarithmic capacity and related functions.

We derive a positive mass theorem for asymptotically flat manifolds with boundary whose mean curvature satisfies a sharp estimate involving the conformal Green's function. The theorem also holds if the conformal Green's function is replaced by the standard Green's function for the Laplacian operator. As an application,…

A mass-type invariant for smooth metric measure spaces and its relation with the fractional Yamabe problem

We construct natural Green forms for special cycles in orthogonal and unitary Shimura varieties, in all codimensions, and, for compact Shimura varieties of type O(p,2) and U(p,1), we show that the resulting local archimedean height pairings are related to special values of derivatives of Siegel Eisentein series. A conj…

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

Green bond leaks impact equity markets, altering investor reactions.

Study characterizes cohomology and homotopy types for M-theory extensions.

This work generalizes a construction by Habermann and Jost of a canonical metric in a Yamabe-positive conformal class, which uses the Green function of the conformal Laplacian. In dimension $n=2k+1$, $2k+2$, or $2k+3$, if the $k$-th GJMS operator $P_k$ admits a Green function, the constant term of its singularity is sh…

AI helps assess nature-related financial risks for financial institutions.

In this paper we study regular irreducible algebraic monoids over $\fldc$ equipped with the euclidean topology. It is shown that, in such monoids, the Green classes and the spaces of idempotents in the Green classes all have natural manifold structures. The interactions of these manifold structures and the semigroup st…

Sharp gradient estimates for positive Ricci curvature manifolds.

Let $π: {\mathbb C}_g \to {\mathbb M}_g$ be the universal family of compact Riemann surfaces of genus $g \geq 1$. We introduce a real-valued function on the moduli space ${\mathbb M}_g$ and compute the first and the second variations of the function. As a consequence we relate the Chern form of the relative tangent bun…

In these lecture notes we discuss the solution theory of geometric wave equations as they arise in Lorentzian geometry: for a normally hyperbolic differential operator the existence and uniqueness properties of Green functions and Green operators is discussed including a detailed treatment of the Cauchy problem on a gl…

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

Study solves a mathematical problem related to elliptic Schroedinger-to-Neumann maps.

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

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

Model shows government incentives boost green bond investment.

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

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

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

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

In the first part of this article we obtain an identity relating the radial spectrum of rotationally invariant geodesic balls and an isoperimetric quotient $\sum 1/λ_{i}^{\rm rad}=\int V(s)/S(s)ds$. We also obtain upper and lower estimates for the series $\sum λ_{i}^{-2}(Ω)$ where $Ω$ is an extrinsic ball of a proper m…

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

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

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

Develops formal moduli theory for splitting complex supermanifolds.

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

The paper investigates quantitative rigidity using Colding's monotonicity formulas for Ricci curvature.

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

Paper models transition risk using jump-diffusion model to price credit swaps.

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.

The Green function on spheres in 3D implies the surface is a round sphere.

Various semigroups of noninvertible supermatrices of the special (antitriangle) shape having nilpotent Berezinian which appear in supersymmetric theories are defined and investigated. A subset of them continuously represents left and right zero semigroups and rectangular bands. The ideal properties of higher order rect…

New estimates for Green's functions in varying Kähler metrics.

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

Discrete Green's functions are the inverses or pseudo-inverses of combinatorial Laplacians. We present compact formulas for discrete Green's functions, in terms of the eigensystems of corresponding Laplacians, for products of regular graphs with or without boundary. Explicit formulas are derived for the cycle, torus, a…

Proves Green function rigidity for specific operators and obtains new ADM mass formula.

Derives formulas from Green function Hessian assumption.

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

Central limit theorem for Green metrics on hyperbolic groups.

The work is motivated by a result of Manin, which relates the Arakelov Green function on a compact Riemann surface to configurations of geodesics in a 3-dimensional hyperbolic handlebody with Schottky uniformization, having the Riemann surface as conformal boundary at infinity. A natural question is to what extent the …

Paper proves inequality for Green function on Kähler manifolds.