On a conformal gap and finiteness theorem for a class of four-manifolds

Sun Yung A. Chang; Jie Qing; Paul Yang

doi:10.1007/s00039-007-0603-1

On a conformal gap and finiteness theorem for a class of four-manifolds

Sun Yung A. Chang, Jie Qing, Paul Yang

Mathematics

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

16 Scopus citations

Abstract

In this paper we develop a bubble tree structure for a degenerating class of Riemannian metrics satisfying some global conformal bounds on compact manifolds of dimension 4. Applying the bubble tree structure, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and make a comparison of the solutions of the σ _k equations on a degenerating family of Bach-flat metrics.

Original language	English (US)
Pages (from-to)	404-434
Number of pages	31
Journal	Geometric and Functional Analysis
Volume	17
Issue number	2
DOIs	https://doi.org/10.1007/s00039-007-0603-1
State	Published - Jun 2007

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

Keywords

Bach-flat metrics
Bubble-tree structure
Curvature concentrations
Finite diffeomorphism theorem
Gap theorem
Neck theorem

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10.1007/s00039-007-0603-1

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title = "On a conformal gap and finiteness theorem for a class of four-manifolds",

abstract = "In this paper we develop a bubble tree structure for a degenerating class of Riemannian metrics satisfying some global conformal bounds on compact manifolds of dimension 4. Applying the bubble tree structure, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and make a comparison of the solutions of the σ k equations on a degenerating family of Bach-flat metrics.",

keywords = "Bach-flat metrics, Bubble-tree structure, Curvature concentrations, Finite diffeomorphism theorem, Gap theorem, Neck theorem",

author = "Chang, {Sun Yung A.} and Jie Qing and Paul Yang",

note = "Funding Information: Keywords and phrases: Bach-flat metrics, curvature concentrations, bubble-tree structure, neck theorem, gap theorem, finite diffeomorphism theorem AMS Mathematics Subject Classification: 53A30, 53C21, 53C24 The first author is supported by NSF Grant DMS–0245266. The second author is supported in part by NSF Grant DMS–0402294. The third author is supported by NSF Grant DMS–0245266.",

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doi = "10.1007/s00039-007-0603-1",

language = "English (US)",

volume = "17",

pages = "404--434",

journal = "Geometric and Functional Analysis",

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T1 - On a conformal gap and finiteness theorem for a class of four-manifolds

AU - Chang, Sun Yung A.

AU - Qing, Jie

AU - Yang, Paul

N1 - Funding Information: Keywords and phrases: Bach-flat metrics, curvature concentrations, bubble-tree structure, neck theorem, gap theorem, finite diffeomorphism theorem AMS Mathematics Subject Classification: 53A30, 53C21, 53C24 The first author is supported by NSF Grant DMS–0245266. The second author is supported in part by NSF Grant DMS–0402294. The third author is supported by NSF Grant DMS–0245266.

PY - 2007/6

Y1 - 2007/6

N2 - In this paper we develop a bubble tree structure for a degenerating class of Riemannian metrics satisfying some global conformal bounds on compact manifolds of dimension 4. Applying the bubble tree structure, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and make a comparison of the solutions of the σ k equations on a degenerating family of Bach-flat metrics.

AB - In this paper we develop a bubble tree structure for a degenerating class of Riemannian metrics satisfying some global conformal bounds on compact manifolds of dimension 4. Applying the bubble tree structure, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and make a comparison of the solutions of the σ k equations on a degenerating family of Bach-flat metrics.

KW - Bach-flat metrics

KW - Bubble-tree structure

KW - Curvature concentrations

KW - Finite diffeomorphism theorem

KW - Gap theorem

KW - Neck theorem

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VL - 17

SP - 404

EP - 434

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 2

ER -

On a conformal gap and finiteness theorem for a class of four-manifolds

Abstract

All Science Journal Classification (ASJC) codes

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