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

176 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

Access to Document

10.2307/3062131

Cite this

@article{9ab515a91f0d4abb90855c3c76190d53,

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.",

author = "Chang, {Sun Yung A.} and Gursky, {Matthew J.} and Yang, {Paul C.}",

year = "2002",

month = may,

doi = "10.2307/3062131",

language = "English (US)",

volume = "155",

pages = "709--787",

journal = "Annals of Mathematics",

issn = "0003-486X",

publisher = "Princeton University Press",

number = "3",

}

TY - JOUR

T1 - An equation of Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature

AU - Chang, Sun Yung A.

AU - Gursky, Matthew J.

AU - Yang, Paul C.

PY - 2002/5

Y1 - 2002/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0036587626&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036587626&partnerID=8YFLogxK

U2 - 10.2307/3062131

DO - 10.2307/3062131

M3 - Article

AN - SCOPUS:0036587626

SN - 0003-486X

VL - 155

SP - 709

EP - 787

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 3

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this