Lack of compactness in conformal metrics with L d/2 curvature

S. Y.A. Chang; M. Gursky; T. Wolff

doi:10.1007/BF02921543

Lack of compactness in conformal metrics with L^d/2 curvature

S. Y.A. Chang, M. Gursky, T. Wolff

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

4 Scopus citations

Abstract

Two examples are given of a sequence on a compact d-dimensional manifold (d ≥ 3) in a fixed conformal class satisfying a uniform L^(d/2) bound on curvature and a bound on volume which are not compact in a C⁰ topology. This shows that the curvature assumption of recent compactness results for conformal metrics is sharp.

Original language	English (US)
Pages (from-to)	143-153
Number of pages	11
Journal	The Journal of Geometric Analysis
Volume	4
Issue number	2
DOIs	https://doi.org/10.1007/BF02921543
State	Published - Jun 1994
Externally published	Yes

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Conformal geometry
Math Subject Classification: 53A30, 53C21
compactness results

Access to Document

10.1007/BF02921543

Cite this

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title = "Lack of compactness in conformal metrics with L d/2 curvature",

abstract = "Two examples are given of a sequence on a compact d-dimensional manifold (d ≥ 3) in a fixed conformal class satisfying a uniform L (d/2) bound on curvature and a bound on volume which are not compact in a C 0 topology. This shows that the curvature assumption of recent compactness results for conformal metrics is sharp.",

keywords = "Conformal geometry, Math Subject Classification: 53A30, 53C21, compactness results",

author = "Chang, {S. Y.A.} and M. Gursky and T. Wolff",

year = "1994",

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doi = "10.1007/BF02921543",

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journal = "The Journal of Geometric Analysis",

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T1 - Lack of compactness in conformal metrics with L d/2 curvature

AU - Chang, S. Y.A.

AU - Gursky, M.

AU - Wolff, T.

PY - 1994/6

Y1 - 1994/6

N2 - Two examples are given of a sequence on a compact d-dimensional manifold (d ≥ 3) in a fixed conformal class satisfying a uniform L (d/2) bound on curvature and a bound on volume which are not compact in a C 0 topology. This shows that the curvature assumption of recent compactness results for conformal metrics is sharp.

AB - Two examples are given of a sequence on a compact d-dimensional manifold (d ≥ 3) in a fixed conformal class satisfying a uniform L (d/2) bound on curvature and a bound on volume which are not compact in a C 0 topology. This shows that the curvature assumption of recent compactness results for conformal metrics is sharp.

KW - Conformal geometry

KW - Math Subject Classification: 53A30, 53C21

KW - compactness results

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