A fully nonlinear version of the Yamabe problem and a Harnack type inequality.

DOI10.1016/S1631-073X(03)00017-7zbMath1113.35069arXivmath/0212031OpenAlexW2021264976MaRDI QIDQ1408077

Aobing Li, Yan-yan Li

Publication date: 15 September 2003

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0212031

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items

Geometric inequalities on locally conformally flat manifolds, Estimates and existence results for a fully nonlinear Yamabe problem on manifolds with boundary, The constraint equations of Lovelock gravity theories: A new σ k-Yamabe problem, Harnack type inequalities for conformal scalar curvature equation, On some conformally invariant fully nonlinear equations. II: Liouville, Harnack and Yamabe, Conformal invariants and partial differential equations

Cites Work

• Unnamed Item
• Liouville-type theorems and harnack-type inequalities for semilinear elliptic equations
• Conformal deformation of a Riemannian metric to constant scalar curvature
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• Conformally flat manifolds, Kleinian groups and scalar curvature
• On some conformally invariant fully nonlinear equations
• An a priori estimate for a fully nonlinear equation on four-manifolds.
• Estimates and existence results for some fully nonlinear elliptic equations on Riemannian manifolds
• Conformal geometry, contact geometry, and the calculus of variations
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Degree Theory for Second Order Nonlinear Elliptic Operators and its Applications
• A fully nonlinear conformal flow on locally conformally flat manifolds
• Some properties of the Schouten tensor and applications to conformal geometry
• Convexity and singularities of curvature equations in conformal geometry