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Based on the uniformization theorems of gravitation instantons by Chen–Chen [Acta Math. 227 (2021), pp. 263–307], Chen–Viaclovsky [Gravitational instantons with quadratic volume growth, 2021], Collins–Jacob–Lin [Forum Math. Sigma (2021)], and Hein–Sun–Viaclovsky–Zhang [Gravitational instantons and del Pezzo surfaces], we prove that the period maps for the , , and gravitational instantons are surjective. In particular, the period domains of these gravitational instantons are exactly their moduli spaces.
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Gravitational instantons with quadratic volume growth
Abstract There are two known classes of gravitational instantons with quadratic volume growth at infinity, known as type and . Gravitational instantons of type were previously classified by Chen–Chen. In this paper, we prove a classification theorem for gravitational instantons. We determine the topology and prove existence of “uniform” coordinates at infinity for both ALG and gravitational instantons. We also prove a result regarding the relationship between ALG gravitational instantons of order and those of order 2.
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- PAR ID:
- 10499668
- Publisher / Repository:
- Oxford University Press (OUP)
- Date Published:
- Journal Name:
- Journal of the London Mathematical Society
- Volume:
- 109
- Issue:
- 4
- ISSN:
- 0024-6107
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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