Gravitational instantons with faster than quadratic curvature decay (II)

Understand

This is our second paper in a series to study gravitational instantons, i.e.

• complete hyperk\"aler 4-manifolds with faster than quadratic curvature decay.
• We prove two main theorems: 1.The asymptotic rate of gravitational instantons to the standard models can be improved automatically.
• 2.Any ALF-D_k gravitational instanton must be the Cherkis-Hitchin-Ivanov-Kapustin-Lindstr\"om-Ro\v{c}ek metric.