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Asymptotic curvature decay and removal of singularities of Bach-flat metrics
Author(s):
Jeffrey
Streets
Journal:
Trans. Amer. Math. Soc.
362
(2010),
1301-1324.
MSC (2000):
Primary 53C25
Posted:
October 20, 2009
MathSciNet review:
2563730
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Abstract:
We prove a removal of singularities result for Bach-flat metrics in dimension  under the assumption of bounded  -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  . 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:
10.1090/S0002-9947-09-04960-5
PII:
S 0002-9947(09)04960-5
Received by editor(s):
September 11, 2007
Posted:
October 20, 2009
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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