Open Access
December 2021 Gravitational instantons with faster than quadratic curvature decay. I
Gao Chen, Xiuxiong Chen
Author Affiliations +
Acta Math. 227(2): 263-307 (December 2021). DOI: 10.4310/ACTA.2021.v227.n2.a2


In this paper, we study gravitational instantons (i.e., complete hyperkähler $4$‑manifolds with faster than quadratic curvature decay). We prove three main theorems: (1) Any gravitational instanton must have one of the following known ends: ALE, ALF, ALG, and ALH. (2) In the ALG and ALH non-splitting cases, it must be biholomorphic to a compact complex elliptic surface minus a divisor. Thus, we confirm a long-standing question of Yau in the ALG and ALH cases. (3) In the ALF‑$D_k$ case, it must have an $O(4)$‑multiplet.


Download Citation

Gao Chen. Xiuxiong Chen. "Gravitational instantons with faster than quadratic curvature decay. I." Acta Math. 227 (2) 263 - 307, December 2021.


Received: 15 November 2018; Published: December 2021
First available in Project Euclid: 1 March 2023

Digital Object Identifier: 10.4310/ACTA.2021.v227.n2.a2

Vol.227 • No. 2 • December 2021
Back to Top