Gravitational instantons with faster than quadratic curvature decay (II)

  • 1 Math Department, Stony Brook University, 100 Nicolls Road, Stony Brook, USA
  • 2 Math Department, Stony Brook University, 100 Nicolls Road, Stony Brook, USA
Gao ChenORCID iD: https://orcid.org/0000-0002-8671-7904 and Xiuxiong Chen

Abstract

This is our second paper in a series to study gravitational instantons, i.e. complete hyperkähler 4-manifolds with faster than quadratic curvature decay. We prove two main theorems: (i) The asymptotic rate of gravitational instantons to the standard models can be improved automatically. (ii) Any ALF-Dk gravitational instanton must be the Cherkis–Hitchin–Ivanov–Kapustin–Lindström–Roček metric.

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