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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Asymptotic curvature decay and removal of singularities of Bach-flat metrics


Author: Jeffrey Streets
Journal: Trans. Amer. Math. Soc. 362 (2010), 1301-1324
MSC (2000): Primary 53C25
DOI: https://doi.org/10.1090/S0002-9947-09-04960-5
Published electronically: October 20, 2009
MathSciNet review: 2563730
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Abstract: We prove a removal of singularities result for Bach-flat metrics in dimension $ 4$ under the assumption of bounded $ L^2$-norm of curvature, bounded Sobolev constant and a volume growth bound. This result extends the removal of singularities result for special classes of Bach-flat metrics obtained by Tian and Viaclovsby. For the proof we emulate Cheeger and Tian and analyze the decay rates of solutions to the Bach-flat equation linearized around a flat metric. This classification is used to prove that Bach-flat cones are in fact ALE of order $ 2$. This result is then used to prove the removal of singularities theorem.


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Additional Information

Jeffrey Streets
Affiliation: Department of Mathematics, Fine Hall, Princeton University, Princeton, New Jersey 08544
Email: jstreets@math.princeton.edu

DOI: https://doi.org/10.1090/S0002-9947-09-04960-5
Received by editor(s): September 11, 2007
Published electronically: October 20, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.