1 February 2024 Torelli-type theorems for gravitational instantons with quadratic volume growth
Gao Chen, Jeff Viaclovsky, Ruobing Zhang
Author Affiliations +
Duke Math. J. 173(2): 227-275 (1 February 2024). DOI: 10.1215/00127094-2023-0020


We prove Torelli-type uniqueness theorems for both ALG gravitational instantons and ALG gravitational instantons which are of order 2. That is, the periods uniquely characterize these types of gravitational instantons up to diffeomorphism. We define a period mapping P, which we show is surjective in the ALG cases, and has open image in the ALG cases. We also construct some new degenerations of hyper-Kähler metrics on the K3 surface which exhibit bubbling of ALG gravitational instantons.


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Gao Chen. Jeff Viaclovsky. Ruobing Zhang. "Torelli-type theorems for gravitational instantons with quadratic volume growth." Duke Math. J. 173 (2) 227 - 275, 1 February 2024. https://doi.org/10.1215/00127094-2023-0020


Received: 17 December 2021; Revised: 19 October 2022; Published: 1 February 2024
First available in Project Euclid: 4 April 2024

MathSciNet: MR4728691
Digital Object Identifier: 10.1215/00127094-2023-0020

Primary: 53C21
Secondary: 53C25 , 53C26 , 53C55

Keywords: gravitational instantons , inhomogeneous collapsing , Ricci-flat metrics , Torelli-type theorems

Rights: Copyright © 2024 Duke University Press

Vol.173 • No. 2 • 1 February 2024
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