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Bach-flat asymptotically locally Euclidean metrics

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Abstract

We obtain a volume growth and curvature decay result for various classes of complete, noncompact Riemannian metrics in dimension 4; in particular our method applies to anti-self-dual or Kähler metrics with zero scalar curvature, and metrics with harmonic curvature. Similar results were obtained for Einstein metrics in [And89], [BKN89], [Tia90], but our analysis differs from the Einstein case in that (1) we consider more generally a fourth order system in the metric, and (2) we do not assume any pointwise Ricci curvature bound.

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  1. Department of Mathematics, MIT, Cambridge, MA, 02139, USA

    Gang Tian & Jeff Viaclovsky

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  1. Gang Tian
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  2. Jeff Viaclovsky
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Correspondence to Gang Tian or Jeff Viaclovsky.

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Tian, G., Viaclovsky, J. Bach-flat asymptotically locally Euclidean metrics. Invent. math. 160, 357–415 (2005). https://doi.org/10.1007/s00222-004-0412-1

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