Obstruction-flat asymptotically locally Euclidean metrics

Abstract

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 $n\ge 3$. 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.

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

References in corpus (1)

• Optimal Curvature Decays on Asymptotically Locally Euclidean Manifolds

Cited by in corpus (1)

• Regularity for Harmonic - Einstein Equation