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arXiv · 2108.12991

Collapsing geometry of hyperkähler 4-manifolds and applications

Song Sun·Ruobing Zhang
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Abstract

We investigate the collapsing geometry of hyperkähler 4-manifolds. As applications we prove 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.

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Song Sun, Ruobing Zhang. 2022-12-29. Collapsing geometry of hyperkähler 4-manifolds and applications. https://arxiv.org/abs/2108.12991

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