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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2604.23410 |
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| _version_ | 1866913062571737088 |
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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 |