Resolution of compact Einstein orbifolds in general dimensions
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918390209183744 |
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| author | Yao, Yichen |
| author_facet | Yao, Yichen |
| contents | Given a noncollapsing sequence of m-dimensional compact Einstein manifolds with a uniform energy bound, the Gromov-Hausdorff limit is a compact Einstein orbifold with at most finitely many singularities. Conversely, starting with a compact Einstein orbifold, we are interested in whether there exists a sequence of smooth Einstein metrics converging to it. In this paper, we provide a negative answer. We give an explicit obstruction for a negative Einstein orbifold appearing as a noncollapsing limit of compact Einstein manifolds, which does not vanish for hyperbolic orbifolds. This work extends the work of Ozuch in dimension 4, with significant technical simplifications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14929 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Resolution of compact Einstein orbifolds in general dimensions Yao, Yichen Differential Geometry Given a noncollapsing sequence of m-dimensional compact Einstein manifolds with a uniform energy bound, the Gromov-Hausdorff limit is a compact Einstein orbifold with at most finitely many singularities. Conversely, starting with a compact Einstein orbifold, we are interested in whether there exists a sequence of smooth Einstein metrics converging to it. In this paper, we provide a negative answer. We give an explicit obstruction for a negative Einstein orbifold appearing as a noncollapsing limit of compact Einstein manifolds, which does not vanish for hyperbolic orbifolds. This work extends the work of Ozuch in dimension 4, with significant technical simplifications. |
| title | Resolution of compact Einstein orbifolds in general dimensions |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2603.14929 |