Collapsing geometry of hyperkähler 4-manifolds and applications
Acta Math., 232 (2024), 325–424
by Song Sun, Ruobing Zhang
Abstract
We investigate the collapsing geometry of hyperkähler 4-manifolds. As applications, we prove the following two well-known conjectures in the field.
(1) Any collapsed limit of unit-diameter hyperkähler metrics on the K3 manifold is isometric to one of the following: the quotient of a flat 3-torus by an involution, a singular special Kähler metric on the 2-sphere, or the unit interval.
(2) Any complete hyperkähler 4-manifold with finite energy (i.e., gravitational instanton) is asymptotic to a model end at infinity.
Published: 30 August 2024
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