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Bibliographic Details
Main Author: Law, Michael B.
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2604.23410
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author Law, Michael B.
author_facet Law, Michael B.
contents Let $(M,g)$ be a complete 4-dimensional Ricci-flat ALE orbifold with finitely many orbifold points and group at infinity $\mathbb{Z}_2$. We prove that if the $L^2$ kernel of its Lichnerowicz Laplacian has dimension at most 3, then $(M,g)$ is either the Eguchi-Hanson space or the flat orbifold $\mathbb{R}^4/\mathbb{Z}_2$. A similar uniqueness result is proved for Calabi's higher-dimensional analogs of the Eguchi-Hanson space among Ricci-flat Kähler ALE orbifolds with group at infinity $\mathbb{Z}_m$.
format Preprint
id arxiv_https___arxiv_org_abs_2604_23410
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle An analytical characterization of Eguchi-Hanson space and its higher-dimensional analogs
Law, Michael B.
Differential Geometry
Mathematical Physics
Let $(M,g)$ be a complete 4-dimensional Ricci-flat ALE orbifold with finitely many orbifold points and group at infinity $\mathbb{Z}_2$. We prove that if the $L^2$ kernel of its Lichnerowicz Laplacian has dimension at most 3, then $(M,g)$ is either the Eguchi-Hanson space or the flat orbifold $\mathbb{R}^4/\mathbb{Z}_2$. A similar uniqueness result is proved for Calabi's higher-dimensional analogs of the Eguchi-Hanson space among Ricci-flat Kähler ALE orbifolds with group at infinity $\mathbb{Z}_m$.
title An analytical characterization of Eguchi-Hanson space and its higher-dimensional analogs
topic Differential Geometry
Mathematical Physics
url https://arxiv.org/abs/2604.23410