A fully nonlinear version of the Yamabe problem on manifolds with boundary

DOI10.4171/JEMS/54zbMath1100.53035OpenAlexW2011350665WikidataQ126113342 ScholiaQ126113342MaRDI QIDQ2502556

Aobing Li, Yan-yan Li

Publication date: 13 September 2006

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/jems/54

zbMATH Keywords

Liouville type theoremsHarnack type inequalities

Mathematics Subject Classification ID

Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (9)

Oblique boundary value problems for augmented Hessian equations. I ⋮ Conformal deformation on manifolds with boundary ⋮ Estimates and existence results for a fully nonlinear Yamabe problem on manifolds with boundary ⋮ Oblique boundary value problems for augmented Hessian equations III ⋮ A fully nonlinear version of the Yamabe problem on locally conformally flat manifolds with umbilic boundary ⋮ From Optimal Transportation to Conformal Geometry ⋮ Counterexamples to C² Boundary Estimates for a Fully Nonlinear Yamabe Problem on Manifolds with Boundary ⋮ Uniqueness theorems for fully nonlinear conformal equations on subdomains of the sphere ⋮ Min-max formulas for nonlocal elliptic operators

Cites Work

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• Uniqueness theorems on conformal deformation of metrics, sobolev inequalities, and an eigenvalue estimate
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• Non—existence of positive solutions to semilinear elliptic equations on r” or r” through the method of moving planes
• On some conformally invariant fully nonlinear equations
• The existence of conformal metrics with constant scalar curvature and constant boundary mean curvature

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