Fully nonlinear equations on Riemannian manifolds with negative curvature

Abstract

We consider the problem of conformally deforming a metric to one with a prescribed symmetric function of the eigenvalues of the Ricci tensor, in the case of negative curvature.

19 pages; final version

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• Local pointwise second derivative estimates for strong solutions to the ${\sigma }_k$-Yamabe equation on Euclidean domains
• A fully nonlinear equation on 4-manifolds with positive scalar curvature
• Geometric inequalities on locally conformally flat manifolds
• Solutions to the ${\sigma }_k$-Loewner-Nirenberg problem on annuli are locally Lipschitz and not differentiable
• On the partial uniform ellipticity and complete conformal metrics with prescribed curvature functions on manifolds with boundary
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