Central limit theorem for Green metrics on hyperbolic groups.
problem Proving a central limit theorem for Green metrics on hyperbolic groups.
method Proving a central limit theorem for Green metrics on hyperbolic groups using probability measures and ordering elements.
result Proved a central limit theorem for Green metrics on hyperbolic groups.
New estimates for Green's functions in varying Kähler metrics.
problem Uniform estimates for Green's functions in Kähler metrics.
method Broadening techniques to allow complex structure variation and removing assumptions.
result Uniform estimates for Green's functions in families of canonical Kähler metrics.
Solves Yamabe problem for 3D metrics of Sobolev class W2,q.
problem Yamabe problem on closed 3-manifolds for Sobolev metrics.
method Developed elliptic theory for conformal Laplacian on rough metrics.
result Existence, regularity, and blow-up analysis for Green function.
The Green's function of a complex plane domain is analyzed with affine scaling.
problem Quantitative properties of the Green's function in multiply connected domains.
method Affine scaling of the domain to study boundary behavior.
result Quantitative boundary behavior of the Green's function and related objects.
Green functions play an important role in conformal geometry. In this paper, we explain how to compute explicitly the logarithmic singularities of the Green functions of the conformal powers of the Laplacian. These operators include the Yamabe and Paneitz operators, as well as the conformal fractional powers of the Lap…
Study curvature estimates for metrics on jet bundles over projective varieties.
problem Curvature estimates for metrics on jet bundles.
method Analogue of Demailly's holomorphic Morse inequalities for invariant jets.
result Analogue of Demailly's results for invariant jets.
In a conformal class of metrics with positive Yamabe invariant, we derive a necessary and sufficient condition for the existence of metrics with positive Q curvature. The condition is conformally invariant. We also prove some inequalities between the Green's functions of the conformal Laplacian operator and the Paneitz…
A mass-type invariant for smooth metric measure spaces and its relation with the fractional Yamabe problem
problem Defining and analyzing a mass-type invariant for smooth metric measure spaces
method Defining a mass-type quantity and showing its geometric invariance properties
result The mass-type quantity has a close relation with the fractional Yamabe problem and the relevant Green's function
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 Pk admits a Green function, the constant term of its singularity is sh…
Extends BV functions and divergence-measure fields to metric spaces.
problem Defining BV functions and divergence-measure fields in metric spaces.
method Employing differential structure developed by N. Gigli, extending BV functions and divergence-measure fields to metric spaces.
result Gauss-Green formulas established for BV functions and divergence-measure fields in metric spaces.
The paper proves complete conformal metrics with negative scalar curvatures have negative Ricci curvatures in convex domains.
problem Negativity of Ricci curvatures in complete conformal metrics.
method Analysis of Green's function and positive mass theorem.
result Complete conformal metrics with negative scalar curvatures have negative Ricci curvatures in convex domains.
Extends Martin boundary to Floyd boundary for random walks.
problem Mapping Martin boundary to Floyd boundary for random walks.
method Continuous equivariant surjection using Green and Floyd metrics.
result Identity map extends to continuous surjection with preimages being singletons.
Develops Green operators for quantum fields on low-regularity spacetimes.
problem Describes quantum fields on low-regularity spacetimes with C1,1 metrics. method Shows well-posedness of wave equation, constructs Green operators, defines symplectic form.
result Provides a locally covariant description of quantum fields.
New proof of Weil-Petersson metric for Calabi-Yau varieties.
problem No specific problem stated; focuses on proof technique.
method Applying Greene-Shapere-Vafa-Yau semi-flat metric.
result Closed formula of Weil-Petersson metric on moduli space of Calabi-Yau varieties.
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 calculates mass and volume of Einstein metrics in four dimensions.
problem Calculating mass and volume of Einstein metrics in four dimensions.
method Using Green's function and conformal laplacian, the paper expresses ADM mass as an integral and proves a mass-volume inequality.
result Proves a lower bound for the mass of a metric in terms of its volume, and various mass gap theorems.
Study spherical metrics on flat torus with cone singularities.
problem Existence and uniqueness of spherical metrics with specific cone angles.
method Analysis of Green function critical points and torus geometry.
result Existence of unique spherical metrics determined by torus geometry.
Paper proves C1,1 regularity for complex Monge-Ampère equations.
problem Complex Monge-Ampère equations on compact almost Hermitian manifolds.
method Proves C1,1 estimate and uses it to show existence of solutions. result Proves C1,1 regularity for geodesics in Sasakian metrics. Green startups in Italy survive longer than non-green ones.
problem Survival of innovative startups in Italy.
method Comparative analysis of green vs. non-green startups in Italy, 2009-2018.
result Green startups are more than twice as likely to survive than non-green ones.
The paper defines and analyzes a new mass function for compact manifolds.
problem Understanding the properties of metrics on compact manifolds.
method Introducing and studying the Mass Function $a \geq 0 \mapsto \xp{M}{a}$ and $\xm{M}{a}$.
result The Mass Functions are well-defined and have properties leading to applications to the Yamabe invariant.
Study on Paneitz operator on standard 3-sphere, deriving variations and invariants.
problem Analyzing the Paneitz operator on the standard 3-sphere.
method Deriving first and second variation formulas for the Green's function pole's value.
result Second variation is nonpositively definite and vanishes only for conformal deformations.
Formula for Hadamard coefficients from Green's operators on spacetimes.
problem Calculating Hadamard coefficients from Green's operators on spacetimes.
method Developed formulas for diagonal values and integrals over the diagonal of Hadamard coefficients.
result Formulated analogues of Hadamard expansions and resolvents for Green's operators.
Paper bounds Kähler manifolds' diameter using Orlicz spaces and complex Monge-Ampère equations.
problem Establishing diameter bounds for Kähler manifolds in Orlicz spaces.
method Proving a priori estimates for solutions of complex Monge-Ampère equations in Orlicz spaces using Kołodziej's and Guo-Phong-Tong-Wang's approaches.
result Uniform estimates for Green's function and its gradient for Kähler metrics.
Green stocks show less factor exposure heterogeneity compared to brown stocks.
problem Exploring differences in factor exposure between green and brown stocks.
method Examined S&P 500 firms grouped by greenhouse gas emissions, analyzing factor exposure over 2014-2020.
result Green stocks have less factor exposure heterogeneity than brown stocks, except for the value factor.
Model shows government incentives boost green bond investment.
problem Increasing green investments through government incentives.
method Optimal incentives indexed on bond prices and covariation, applied to a portfolio of bonds.
result Method outperforms current tax-incentives systems in green investments.
Green functions on stationary varifolds established with inequalities and convergence results.
problem Establishing Green functions on stationary varifolds with inequalities and convergence.
method Extending Grüter and Widman's method, constructing Green functions, using local Harnack inequality.
result Green functions converge for sequences of stationary varifolds converging with multiplicity one.
The Green function helps in creating evenly spaced points on compact manifolds.
problem Creating evenly spaced points on compact manifolds.
method Using the Green function for the Laplacian to minimize energy and achieve uniform distribution.
result A sequence of minimizers for the Green energy is asymptotically uniformly distributed.
The paper derives expansions for Green's operators and resolvents using Hadamard methods.
problem Analyzing normally hyperbolic operators and their Green's functions.
method Hadamard expansions for powers of Green's operators and resolvents.
result Derives expansions involving Hadamard coefficients for advanced/retarded Green's operators.
Paper extends Green-Osher inequality for convex bodies at dilation position.
problem Extending Green-Osher inequality for specific geometric configurations.
method Analyzes strictly convex bodies at dilation position and derives necessary and sufficient conditions.
result Establishes extended Green-Osher inequality with conditions for equality.
Mathematical analysis of Riemann surfaces and their moduli spaces using hybrid Laplacians.
problem Analyzing the asymptotics of Arakelov Green functions on Riemann surfaces near boundary of moduli spaces.
method Introducing hybrid Laplacian, solving hybrid Poisson equation, and defining hybrid Green functions.
result Layered description of asymptotics of Arakelov Green functions on Riemann surfaces near boundary of their moduli spaces.
The paper provides formulas for Hadamard coefficients using Green's operators.
problem Calculating Hadamard coefficients from Green's operators.
method Various methods including resolvents, powers of Green's operators, and product with the real line.
result Formulas for Hadamard coefficients in terms of Green's operators.
The paper discusses methods to compute Green's function on algebraic surfaces using Schottky uniformization.
problem Computing Green's function on algebraic surfaces using Schottky uniformization.
method Investigates convergence of deformations of a formula related to Green's function.
result Provides insights into the geometric interpretation of the formula for Green's function.
A new approach for green investing in Indian markets considers environmental factors.
problem Identifying and managing climate risk in sustainable investing.
method Combining ESG ratings with modern portfolio theory and scenario analysis.
result The green portfolio performs better than market returns, highlighting the importance of climate risk.
A regression algorithm uses Green's function and covariance matrix for predictive distributions.
problem Regression and uncertainty quantification for machine learning.
method Green's function theory, Bayesian approach, covariance matrix of normalized Green's function.
result The covariance matrix provides predictive distributions with mean and confidence intervals.
Gauss-Green theorem proven for vector fields in stratified groups.
problem Establishing the Gauss-Green theorem for vector fields in noncommutative stratified Lie groups.
method Developed a new family of function spaces for divergence-measure fields and proved the Gauss-Green theorem.
result Gauss-Green theorem achieved for vector fields of low regularity on sets of finite perimeter in stratified groups.
Study on p-Green functions on specific manifolds, proving monotonicity.
problem Monotonicity of p-Green functions on certain 3D manifolds. method Sharp monotonicity formula for p-Green functions along level sets. result Established monotonicity for 1<p<3 on specific manifolds. Improved estimates for p-Green functions near poles in Euclidean and Riemannian settings.
problem Asymptotic behavior of p-Green functions near poles.
method Asymptotic expansion and integrability properties for derivatives.
result Improved estimates and asymptotic expansions for p-Green functions.
Margin trading and short selling boost green tech innovation in China.
problem Encouraging green technology innovation in Chinese companies.
method Quasi-experimental research using panel data of Chinese listed companies, double difference model.
result Margin trading and short selling increase green tech innovation significantly.
On compact surfaces, a Green-Wasserstein inequality cannot be improved without the sqrt(log n) factor.
problem Can the Green-Wasserstein inequality be improved without the sqrt(log n) factor?
method Contradiction proof using second-moment estimates and semi-discrete random matching asymptotics.
result It is impossible to remove the sqrt(log n) factor in the inequality on any compact connected surface.
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.
problem Risk spillovers among AI ETFs, AI tokens, and green markets.
method R2 decomposition method
result AI ETFs and clean energy act as risk transmitters, while AI tokens and green assets act as receivers.
Green functions for GJMS operators on spheres derived, linking geometry and rigidity.
problem Deriving Green functions for GJMS operators on spheres.
method Explicit representation formulae derived using Gegenbauer polynomials.
result Spheres uniquely characterized by their Green functions, with strong rigidity theorems for n=3,4,5. Survey on rigidity and almost rigidity of Green functions in non-negative Ricci curvature spaces.
problem Rigidity and almost rigidity of Green functions in non-negative Ricci curvature spaces.
method Survey and observation on Cheeger-Yau inequality on RCD spaces.
result Observations on the Cheeger-Yau inequality and its applications.
Green bond leaks impact equity markets, altering investor reactions.
problem Green bond leaks affect equity market reactions.
method Identified 259 instances of pre-announcement leaks in 2,036 green bond headlines.
result News leaks significantly alter equity trading dynamics and investor reactions.
The Green function on spheres in 3D implies the surface is a round sphere.
problem Verifying a conjecture about the Green function on spheres.
method Analyzing the Green function form and its properties on a sphere.
result Closed C2 embedded surfaces with the specified Green function are necessarily round spheres. Proves unique Kähler-Einstein metric on certain manifolds.
problem Negative curvature Kähler manifolds.
method Holomorphic curvature bounds, uniqueness proof.
result Uniform equivalence of metrics on manifolds.
New proof of Suita's conjecture without L2 extension theorem.
problem Equality in Suita's conjecture for open Riemann surfaces.
method Exploration of Maitani and Yamaguchi's variation formula for the Bergman kernel and harmonicity.
result Characterization of surfaces by constant Gaussian curvature properties of the Bergman kernel or metric.
Study asymptotics of Poisson kernel and Green's functions for fractional conformal Laplacian.
problem Asymptotics of Poisson kernel and Green's functions for fractional conformal Laplacian.
method Sharp expansions derived for the Poisson kernel and Green's functions near singularities.
result Sharp expansions of the Green's functions solve the first part of Kim-Musso-Wei's conjecture.