arXiv research

Uniform bounds for Green's function on Kähler manifolds derived from complex Monge-Ampère equations.

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

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

This is the first paper in a series of investigation of the pluripotential theory on Teichmüller space. The main purpose of this paper is to give an alternative approach to the Krushkal formula of the pluricomplex Green function on Teichmüller space. We also show that Teichmüller space carries a natural stratified stru…

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…

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…

In this paper we prove a uniform estimate for the gradient of the Green function on a closed Riemann surface, independent of its conformal class, and we derive compactness results for immersions with L2-bounded second fundamental form and for riemannian surfaces of uniformly bounded gaussian curvature entropy.

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…

We obtain an explicit formula for the symplectic form over the double quotient with help of the Green function of a Riemann surface.

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…

Infinitesimal variation of Action functional in classical (non-quantum) field theory with higher derivatives is presented in terms of well-defined intrinsic geometric objects independent of the particular field which varies. 'Integration by parts' procedure for this variation is then described in purely formal language…

It has been shown that the Alvarez-Gaum$\mathrm{\acute{e}}$-Witten miraculous anomaly cancellation formula in type IIB superstring theory and its various generalizations can be derived from modularity of certain characteristic forms. In this paper, we show that the Green-Schwarz formula and the Schwarz-Witten formula i…

The paper proves inequalities for twisted differential forms on manifolds.

The paper analyzes how ESG investors can prioritize green stocks without sacrificing overall wealth.

We prove a stability result for volume forms on fiber bundles with compact base and noncompact fibers. This generalizes the classical results of Moser and Greene--Shiohama, and recent work by the authors.

Continuous family of elliptic operators' projections maintain Cauchy data spaces.

It is shown that, on a compact Kahler manifold with boundary, the singularities of the pluricomplex Green's function with multiple poles can be prescribed to be of the form $\log\sum_{j=1}^n|f_j(z)|^2$ at each pole, where $f_j(z)$ are arbitrary local holomorphic functions with the pole as their only common zero. The pr…

Using generalized Riemann maps, normal forms for almost complex domains (D, J) with singular foliations by stationary disks are defined. Such normal forms are used to construct counterexamples and to determine intrinsic conditions, under which the stationary disks are extremal disks for the Kobayashi metric or determin…

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

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.

Using the Fourier analysis techniques on hyperbolic spaces and Green's function estimates, we confirm in this paper the conjecture given by the same authors in [43]. Namely, we prove that the sharp constant in the $\frac{n-1}{2}$-th order Hardy-Sobolev-Maz'ya inequality in the upper half space of dimension $n$ coincide…

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.

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…

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

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

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.

Green bond leaks impact equity markets, altering investor reactions.

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

We give background which shows the connection between the mean value theorem and the obstacle problem, and then we prove that a set is a mean value set for an elliptic operator of the form $Lu := \partial_i (a^{ij}(x) \partial_j u(x))$ if and only if it arises as the noncontact set of an obstacle problem involving the …

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.

New eco-systemic prudential policies aim to finance green companies, reducing systemic financial risk.

We construct contact forms with constant $Q^\prime$-curvature on compact three-dimensional CR manifolds which admit a pseudo-Einstein contact form and satisfy some natural positivity conditions. These contact forms are obtained by minimizing the CR analogue of the $II$-functional from conformal geometry. Two crucial st…

We construct contact forms with constant $Q^\prime$-curvature on compact three-dimensional CR manifolds which admit a pseudo-Einstein contact form and satisfy some natural positivity conditions. These contact forms are obtained by minimizing the CR analogue of the $II$-functional from conformal geometry. Two crucial st…

Derives formulas from Green function Hessian assumption.