Obstruction-flat asymptotically locally Euclidean metrics

Details Obstruction-flat asymptotically locally Euclidean metrics Obstruction-flat asymptotically locally Euclidean metrics

2011-06-07

arxiv.org/abs/1106.1249v2

Mathematics

Differential Geometry

43 pages; revised version to appear in Geometric and Functional Analysis

Scientific paper

We show that any asymptotically locally Euclidean (ALE) metric which is obstruction-flat or extended obstruction-flat must be ALE of a certain optimal order. Moreover, our proof applies to very general elliptic systems and in any dimension $n \geq 3$. The proof is based on the technique of Cheeger-Tian for Ricci-flat metrics. We also apply this method to obtain a singularity removal theorem for (extended) obstruction-flat metrics with isolated $C^0$-orbifold singular points.

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