Compactness of solutions to the Yamabe problem. III

Yan Yan Li; Lei Zhang

doi:10.1016/j.jfa.2006.11.010

Compactness of solutions to the Yamabe problem. III

Yan Yan Li, Lei Zhang

School of Arts and Sciences, Mathematics

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

54 Scopus citations

Abstract

For a sequence of blow up solutions of the Yamabe equation on non-locally conformally flat compact Riemannian manifolds of dimension 10 or 11, we establish sharp estimates on its asymptotic profile near blow up points as well as sharp decay estimates of the Weyl tensor and its covariant derivatives at blow up points. If the Positive Mass Theorem held in dimensions 10 and 11, these estimates would imply the compactness of the set of solutions of the Yamabe equation on such manifolds.

Original language	English (US)
Pages (from-to)	438-474
Number of pages	37
Journal	Journal of Functional Analysis
Volume	245
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2006.11.010
State	Published - Apr 15 2007

All Science Journal Classification (ASJC) codes

Analysis

Keywords

Compactness of solutions
Yamabe problem

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10.1016/j.jfa.2006.11.010

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title = "Compactness of solutions to the Yamabe problem. III",

abstract = "For a sequence of blow up solutions of the Yamabe equation on non-locally conformally flat compact Riemannian manifolds of dimension 10 or 11, we establish sharp estimates on its asymptotic profile near blow up points as well as sharp decay estimates of the Weyl tensor and its covariant derivatives at blow up points. If the Positive Mass Theorem held in dimensions 10 and 11, these estimates would imply the compactness of the set of solutions of the Yamabe equation on such manifolds.",

keywords = "Compactness of solutions, Yamabe problem",

author = "Li, {Yan Yan} and Lei Zhang",

note = "Funding Information: * Corresponding author. E-mail addresses: yyli@math.rutgers.edu (Y.Y. Li), leizhang@math.ufl.edu (L. Zhang). 1 Part of the work is supported by NSF-DMS-0401118. 2 Part of the work is supported by NSF-DMS-0600275.",

year = "2007",

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doi = "10.1016/j.jfa.2006.11.010",

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T1 - Compactness of solutions to the Yamabe problem. III

AU - Li, Yan Yan

AU - Zhang, Lei

N1 - Funding Information: * Corresponding author. E-mail addresses: yyli@math.rutgers.edu (Y.Y. Li), leizhang@math.ufl.edu (L. Zhang). 1 Part of the work is supported by NSF-DMS-0401118. 2 Part of the work is supported by NSF-DMS-0600275.

PY - 2007/4/15

Y1 - 2007/4/15

N2 - For a sequence of blow up solutions of the Yamabe equation on non-locally conformally flat compact Riemannian manifolds of dimension 10 or 11, we establish sharp estimates on its asymptotic profile near blow up points as well as sharp decay estimates of the Weyl tensor and its covariant derivatives at blow up points. If the Positive Mass Theorem held in dimensions 10 and 11, these estimates would imply the compactness of the set of solutions of the Yamabe equation on such manifolds.

AB - For a sequence of blow up solutions of the Yamabe equation on non-locally conformally flat compact Riemannian manifolds of dimension 10 or 11, we establish sharp estimates on its asymptotic profile near blow up points as well as sharp decay estimates of the Weyl tensor and its covariant derivatives at blow up points. If the Positive Mass Theorem held in dimensions 10 and 11, these estimates would imply the compactness of the set of solutions of the Yamabe equation on such manifolds.

KW - Compactness of solutions

KW - Yamabe problem

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DO - 10.1016/j.jfa.2006.11.010

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VL - 245

SP - 438

EP - 474

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

Compactness of solutions to the Yamabe problem. III

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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