Period domains for gravitational instantons

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.