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

Sun Yung A. Chang; Matthew J. Gursky; Paul C. Yang

doi:10.2307/3062131

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

Sun Yung A. Chang, Matthew J. Gursky, Paul C. Yang

Mathematics

Research output: Contribution to journal › Article › peer-review

163 Scopus citations

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.

Original language	English (US)
Pages (from-to)	709-787
Number of pages	79
Journal	Annals of Mathematics
Volume	155
Issue number	3
DOIs	https://doi.org/10.2307/3062131
State	Published - May 2002

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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title = "An equation of Monge-Amp{\`e}re type in conformal geometry, and four-manifolds of positive Ricci curvature",

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.",

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

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