Gravitational instantons with quadratic volume growth
Gao Chen, Jeff Viaclovsky
Abstract
There are two known classes of gravitational instantons with quadratic volume growth at infinity, known as type ALG and ALG$^*$. Gravitational instantons of type ALG were previously classified by Chen-Chen. In this paper, we prove a classification theorem for ALG$^*$ gravitational instantons. We determine the topology and prove existence of "uniform" coordinates at infinity for both ALG and ALG$^*$ gravitational instantons. We also prove a result regarding the relationship between ALG gravitational instantons of order $\mathfrak{n}$ and those of order $2$.