Period domains for gravitational instantons

Abstract

Based on the uniformization theorems of gravitation instantons by Chen--Chen arXiv:1505.01790, Chen--Viaclovsky arXiv:2110.06498, Collins--Jacob--Lin arXiv:2111.09260, and Hein--Sun--Viaclovsky--Zhang arXiv:2111.09287, we prove that the period maps for the ALH*, ALG, and ALG* gravitational instantons are surjective.

arXiv comment41 pages and 2 figures. Comments are welcome! In this version, we corrected some typos, changed some notation, and re-write Section 2.5 as well as Lemma A.2