Existence and Uniqueness of Green's Functions to Nonlinear Yamabe Problems

DOI10.1002/cpa.22044arXiv2001.00993OpenAlexW4220862524MaRDI QIDQ6095150

No author found.

Publication date: 11 October 2023

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.00993

zbMATH Keywords

conformal metricsGreen functionSchouten tensorasymptotically flat endsnonlinear Yamabe problems

Mathematics Subject Classification ID

Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Conformal structures on manifolds (53C18)

Related Items

Differential inclusions for the Schouten tensor and nonlinear eigenvalue problems in conformal geometry ⋮ Interior regularity for strong solutions to a class of fully nonlinear elliptic equations ⋮ Regularity of viscosity solutions of the σk$\sigma _k$‐Loewner–Nirenberg problem ⋮ Augmented Hessian equations on Riemannian manifolds: from integral to pointwise local second derivative estimates ⋮ On the σκ -Nirenberg problem ⋮ Critical metrics for log-determinant functionals in conformal geometry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Dirichlet problem with prescribed interior singularities
• A generalized mass involving higher order symmetric functions of the curvature tensor
• A new mass for asymptotically flat manifolds
• Solving the degenerate complex Monge-Ampère equation with one concentrated singularity
• Solutions of some Monge-Ampère equations with isolated and line singularities
• A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity
• Degenerate conformally invariant fully nonlinear elliptic equations
• A compactness theorem for the Yamabe problem
• Blow-up phenomena for the Yamabe equation. II
• On Harnack inequalities and singularities of admissible metrics in the Yamabe problem
• Regularity for a class of nonlinear elliptic systems
• Relative volume comparison with integral curvature bounds
• Comparison principles and Lipschitz regularity for some nonlinear degenerate elliptic equations
• An a priori estimate for a fully nonlinear equation on four-manifolds.
• A new proof of local \(C^{1,\alpha}\) regularity for solutions of certain degenerate elliptic P.D.E
• An equation of Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature
• Prescribing scalar curvature on \(\mathbb{S}^ n\) and related problems. I
• Hessian measures. II
• Conformal geometry, contact geometry, and the calculus of variations
• A priori estimates and existence for a class of fully nonlinear elliptic equations in conformal geometry
• A compactness theorem for a fully nonlinear Yamabe problem under a lower Ricci curvature bound
• Prescribing symmetric functions of the eigenvalues of the Ricci tensor
• On some conformally invariant fully nonlinear equations. II: Liouville, Harnack and Yamabe
• Linear and quasilinear elliptic equations
• On conformally-flat spaces in the large
• Harmonische Abbildungen und die Differentialgleichung \(rt-s^2=1\)
• The Gauss–Bonnet–Chern Mass of Conformally Flat Manifolds
• Harnack Inequalities and Bôcher-Type Theorems for Conformally Invariant, Fully Nonlinear Degenerate Elliptic Equations
• Fundamental solutions of homogeneous fully nonlinear elliptic equations
• $C^\infty$ approximations of convex, subharmonic, and plurisubharmonic functions
• Coordinate Invariance and Energy Expressions in General Relativity
• Towards a Liouville Theorem for Continuous Viscosity Solutions to Fully Nonlinear Elliptic Equations in Conformal Geometry
• C1 + α local regularity of weak solutions of degenerate elliptic equations
• The Yamabe problem
• Smoothness of Certain Degenerate Elliptic Equations
• On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
• On some conformally invariant fully nonlinear equations
• Analysis and geometry on manifolds with integral Ricci curvature bounds. II
• Some properties of the Schouten tensor and applications to conformal geometry
• CALCULUS, HEAT FLOW AND CURVATURE-DIMENSION BOUNDS IN METRIC MEASURE SPACES
• Conformal metrics with prescribed curvature functions on manifolds with boundary
• Local gradient estimates of solutions to some conformally invariant fully nonlinear equations
• Riemannian geometry
• Isolated singularities for fully nonlinear elliptic equations