Riemannian Manifolds with Positive Yamabe Invariant and Paneitz Operator

Matthew J. Gursky, Fengbo Hang, Yueh Ju Lin

Research output: Contribution to journalArticle

Abstract

For a Riemannian manifold with dimension at least 6, we prove that the existence of a conformal metric with positive scalar and Q curvature is equivalent to the positivity of both the Yamabe invariant and the Paneitz operator.

Original languageEnglish (US)
Pages (from-to)1348-1367
Number of pages20
JournalInternational Mathematics Research Notices
Volume2016
Issue number5
DOIs
StatePublished - Jun 19 2016

Fingerprint

Q-curvature
Conformal Metric
Positive Scalar Curvature
Positivity
Riemannian Manifold
Invariant
Operator

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Riemannian Manifolds with Positive Yamabe Invariant and Paneitz Operator. / Gursky, Matthew J.; Hang, Fengbo; Lin, Yueh Ju.

In: International Mathematics Research Notices, Vol. 2016, No. 5, 19.06.2016, p. 1348-1367.

Research output: Contribution to journalArticle

@article{ac6fa6906e9e429d919a774d4e895693,
title = "Riemannian Manifolds with Positive Yamabe Invariant and Paneitz Operator",
abstract = "For a Riemannian manifold with dimension at least 6, we prove that the existence of a conformal metric with positive scalar and Q curvature is equivalent to the positivity of both the Yamabe invariant and the Paneitz operator.",
author = "Gursky, {Matthew J.} and Fengbo Hang and Lin, {Yueh Ju}",
year = "2016",
month = "6",
day = "19",
doi = "10.1093/imrn/rnv176",
language = "English (US)",
volume = "2016",
pages = "1348--1367",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",
number = "5",

}

TY - JOUR

T1 - Riemannian Manifolds with Positive Yamabe Invariant and Paneitz Operator

AU - Gursky, Matthew J.

AU - Hang, Fengbo

AU - Lin, Yueh Ju

PY - 2016/6/19

Y1 - 2016/6/19

N2 - For a Riemannian manifold with dimension at least 6, we prove that the existence of a conformal metric with positive scalar and Q curvature is equivalent to the positivity of both the Yamabe invariant and the Paneitz operator.

AB - For a Riemannian manifold with dimension at least 6, we prove that the existence of a conformal metric with positive scalar and Q curvature is equivalent to the positivity of both the Yamabe invariant and the Paneitz operator.

UR - http://www.scopus.com/inward/record.url?scp=84973390121&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84973390121&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnv176

DO - 10.1093/imrn/rnv176

M3 - Article

VL - 2016

SP - 1348

EP - 1367

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 5

ER -