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arXiv · 2604.23410

An analytical characterization of Eguchi-Hanson space and its higher-dimensional analogs

Michael B. Law
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Abstract

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 K\"ahler ALE orbifolds with group at infinity $\mathbb{Z}_m$.

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Michael B. Law. 2026-04-25. An analytical characterization of Eguchi-Hanson space and its higher-dimensional analogs. https://arxiv.org/abs/2604.23410

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