The large scale structure of complete $4$-manifolds with nonnegative Ricci curvature and Euclidean volume growth
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910911433801728 |
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| author | Semola, Daniele |
| author_facet | Semola, Daniele |
| contents | We survey the implications of our joint work with E. Bruè and A. Pigati on the structure of blow-downs for a smooth, complete, Riemannian $4$-manifold with nonnegative Ricci curvature and Euclidean volume growth. Very imprecisely, any such manifold looks like a cone over a spherical space form at infinity. We present some open questions and discuss possible future directions along the way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07125 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The large scale structure of complete $4$-manifolds with nonnegative Ricci curvature and Euclidean volume growth Semola, Daniele Differential Geometry Metric Geometry 53C23 We survey the implications of our joint work with E. Bruè and A. Pigati on the structure of blow-downs for a smooth, complete, Riemannian $4$-manifold with nonnegative Ricci curvature and Euclidean volume growth. Very imprecisely, any such manifold looks like a cone over a spherical space form at infinity. We present some open questions and discuss possible future directions along the way. |
| title | The large scale structure of complete $4$-manifolds with nonnegative Ricci curvature and Euclidean volume growth |
| topic | Differential Geometry Metric Geometry 53C23 |
| url | https://arxiv.org/abs/2501.07125 |