Existence and Uniqueness of Green's Functions to Nonlinear Yamabe Problems
type: Item
instance of: scholarly article
title: Existence and Uniqueness of Green's Functions to Nonlinear Yamabe Problems
arXiv ID: 2001.00993
published in: Communications on Pure and Applied Mathematics
publication date: 2023-10-11T00:00:00Z
full work available at URL: https://arxiv.org/abs/2001.00993
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 53C23
Mathematics Subject Classification ID: 53C18
Mathematics Subject Classification ID: 58J60
zbMATH DE Number: 7748322
zbMATH Keywords: conformal metrics
zbMATH Keywords: Schouten tensor
zbMATH Keywords: asymptotically flat ends
zbMATH Keywords: Green function
zbMATH Keywords: nonlinear Yamabe problems
MaRDI profile type: Publication
OpenAlex ID: W4220862524
cites work: CALCULUS, HEAT FLOW AND CURVATURE-DIMENSION BOUNDS IN METRIC MEASURE SPACES
cites work: Fundamental solutions of homogeneous fully nonlinear elliptic equations
cites work: Coordinate Invariance and Energy Expressions in General Relativity
cites work: Blow-up phenomena for the Yamabe equation. II
cites work: A course in metric geometry
cites work: A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity
cites work: Q4855688
cites work: An a priori estimate for a fully nonlinear equation on four-manifolds.
cites work: An equation of Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature
cites work: Q3378986
cites work: On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
cites work: C1 + α local regularity of weak solutions of degenerate elliptic equations
cites work: A new proof of local \(C^{1,\alpha}\) regularity for solutions of certain degenerate elliptic P.D.E
cites work: Q3134551
cites work: Riemannian geometry
cites work: A new mass for asymptotically flat manifolds
cites work: The Gauss-Bonnet-Chern mass of conformally flat manifolds
cites work: $C^\infty$ approximations of convex, subharmonic, and plurisubharmonic functions
cites work: Conformal metrics with prescribed curvature functions on manifolds with boundary
cites work: Some properties of the Schouten tensor and applications to conformal geometry
cites work: Q4808270
cites work: Prescribing symmetric functions of the eigenvalues of the Ricci tensor
cites work: The Dirichlet problem with prescribed interior singularities
cites work: Solutions of some Monge-Ampère equations with isolated and line singularities
cites work: Harmonische Abbildungen und die Differentialgleichung \(rt-s^2=1\)
cites work: A compactness theorem for the Yamabe problem
cites work: On conformally-flat spaces in the large
cites work: Isolated singularities for fully nonlinear elliptic equations
cites work: Linear and quasilinear elliptic equations
cites work: The Yamabe problem
cites work: Solving the degenerate complex Monge-Ampère equation with one concentrated singularity
cites work: Smoothness of Certain Degenerate Elliptic Equations
cites work: Prescribing scalar curvature on \(\mathbb{S}^ n\) and related problems. I
cites work: Degenerate conformally invariant fully nonlinear elliptic equations
cites work: Local gradient estimates of solutions to some conformally invariant fully nonlinear equations
cites work: On some conformally invariant fully nonlinear equations
cites work: On some conformally invariant fully nonlinear equations. II: Liouville, Harnack and Yamabe
cites work: A generalized mass involving higher order symmetric functions of the curvature tensor
cites work: A compactness theorem for a fully nonlinear Yamabe problem under a lower Ricci curvature bound
cites work: Harnack inequalities and Bôcher-type theorems for conformally invariant, fully nonlinear degenerate elliptic equations
cites work: Comparison principles and Lipschitz regularity for some nonlinear degenerate elliptic equations
cites work: Towards a Liouville Theorem for Continuous Viscosity Solutions to Fully Nonlinear Elliptic Equations in Conformal Geometry
cites work: Q4183803
cites work: Relative volume comparison with integral curvature bounds
cites work: Analysis and geometry on manifolds with integral Ricci curvature bounds. II
cites work: Q5599348
cites work: Hessian measures. II
cites work: On Harnack inequalities and singularities of admissible metrics in the Yamabe problem
cites work: Regularity for a class of nonlinear elliptic systems
cites work: Q5597752
cites work: Conformal geometry, contact geometry, and the calculus of variations
cites work: A priori estimates and existence for a class of fully nonlinear elliptic equations in conformal geometry
cites work: Q3525214
DOI: 10.1002/CPA.22044
Recommended article: Q4867595
Recommended article: Estimates on the Green Function and Existence of Positive Solutions of Nonlinear Singular Elliptic Equations
Recommended article: Q4207069
Recommended article: Existence and uniqueness of solution to nonlinear boundary value problems with sign-changing Green's function
Recommended article: Q3001447
Recommended article: Estimates on the Green's function and existence of positive solutions of nonlinear singular elliptic equations in the half space
Recommended article: Yamabe type equations with sign-changing nonlinearities on the Heisenberg group, and the role of Green functions

Existence and Uniqueness of Green's Functions to Nonlinear Yamabe Problems (Recommended article)
Recommended article: Green's function and an inequality of Lyapunov-type for conformable boundary value problem
Similarity Score: 0.89056873
Recommender Run: Recommender Run 2

Existence and Uniqueness of Green's Functions to Nonlinear Yamabe Problems (Recommended article)
Recommended article: Q5234586
Similarity Score: 0.8904131
Recommender Run: Recommender Run 2

Existence and Uniqueness of Green's Functions to Nonlinear Yamabe Problems (Recommended article)
Recommended article: Q3368562
Similarity Score: 0.8900975
Recommender Run: Recommender Run 2