An equation of Monge-Ampere type in conformal geometry, and four-manifolds of positive Ricci curvature

2004/09/29 by Sun-Yung A. Chang, Matthew J. Gursky, Paul C. Yang · 2 citations
Mathematics · #math.DG #math.AP

paper · pdf

published as Ann. of Math. (2), Vol. 155 (2002), no. 3, 709--787 · 79 pages, published version

arxiv created 2004/09/29 · arxiv updated 2009/12/01

Abstract

We formulate natural conformally invariant conditions on a 4-manifold for the existence of a metric whose Schouten tensor satisfies a quadratic inequality. This inequality implies that the eigenvalues of the Ricci tensor are positively pinched.

Cited by

• Fully nonlinear prescribed curvature problems on closed manifolds with negative curvature
• The σ_k-Loewner-Nirenberg problem on Riemannian manifolds for k=(n)/(2) and beyond

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