Regularity of viscosity solutions of the σk$\sigma _k$‐Loewner–Nirenberg problem

DOI10.1112/plms.12536arXiv2203.05254MaRDI QIDQ6075088

Jingang Xiong, Yan-yan Li, Luc Nguyen

Publication date: 20 September 2023

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.05254

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Viscosity solutions to PDEs (35D40) Singular elliptic equations (35J75)

Related Items

Differential inclusions for the Schouten tensor and nonlinear eigenvalue problems in conformal geometry ⋮ On fully nonlinear Loewner-Nirenberg problem of Ricci curvature

Cites Work

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• Complete conformal metrics of negative Ricci curvature on Euclidean spaces
• Existence of complete conformal metrics of negative Ricci curvature on manifolds with boundary
• Complete conformal metrics with negative scalar curvature in compact Riemannian manifolds
• Singularités éliminables d'équations elliptiques non linéaires
• On the regularity of solutions to the Yamabe equation and the existence of smooth hyperboloidal initial data for Einstein's field equations
• Monge-Ampère equations, the Bergman kernel, and geometry of pseudoconvex domains
• Elliptic partial differential equations of second order
• Comparison principles and Lipschitz regularity for some nonlinear degenerate elliptic equations
• Weakly asymptotically hyperbolic manifolds
• Existence and uniqueness to a fully nonlinear version of the Loewner-Nirenberg problem
• Deforming metrics with negative curvature by a fully nonlinear flow
• Renormalized volume
• Boundary expansion for the Loewner-Nirenberg problem in domains with conic singularities
• Boundary expansions of complete conformal metrics with negative Ricci curvatures
• The Loewner-Nirenberg problem in singular domains
• Classification of singular radial solutions to the \(\sigma_k\) Yamabe equation on annular domains
• Sets of Finite Perimeter and Geometric Variational Problems
• Volume renormalization for singular Yamabe metrics
• An invariant related to the existence of conformally compact Einstein fillings
• Complete Conformal Metrics of Negative Ricci Curvature on Compact Manifolds with Boundary
• Boundaries of Caccioppoli sets with Hölder-continuois normal vector.
• A study of the singularities of solutions of a class of nonlinear elliptic partial differential equation
• Existence of positive solutions to with prescribed singularities and their geometric implications
• Fully nonlinear equations on Riemannian manifolds with negative curvature
• Solutions to the σ_k-Loewner-Nirenberg Problem on Annuli are Locally Lipschitz and Not Differentiable
• Small Perturbation Solutions for Elliptic Equations
• Local gradient estimates of solutions to some conformally invariant fully nonlinear equations
• Existence and Uniqueness of Green's Functions to Nonlinear Yamabe Problems