  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.
