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arXiv · 2110.06498

Gravitational instantons with quadratic volume growth

Gao Chen·Jeff Viaclovsky
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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 $2$.

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Gao Chen, Jeff Viaclovsky. 2021-10-13. Gravitational instantons with quadratic volume growth. https://arxiv.org/abs/2110.06498

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