Geometric Structure of Ends of Ricci Shrinkers
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911105656291328 |
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| author | Bertellotti, Alessandro Buzano, Reto |
| author_facet | Bertellotti, Alessandro Buzano, Reto |
| contents | We study blow-up sequences of Ricci shrinkers without global curvature assumptions based at points $q$ at which the scalar curvature satisfies a Type I bound, proving that their $\mathbb{F}$-limits split a line. In the four-dimensional case these limits are smooth Ricci shrinkers and the convergence is in the pointed smooth Cheeger-Gromov sense. As a consequence, limits along the integral curve of $\nabla f$ starting at such a point $q$ split a line. This generalises known results about the geometry of ends of Ricci shrinkers that relied on global curvature bounds. To obtain our results, we extend the $\mathbb{F}$-convergence theory from Bamler and Li-Wang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10790 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric Structure of Ends of Ricci Shrinkers Bertellotti, Alessandro Buzano, Reto Differential Geometry We study blow-up sequences of Ricci shrinkers without global curvature assumptions based at points $q$ at which the scalar curvature satisfies a Type I bound, proving that their $\mathbb{F}$-limits split a line. In the four-dimensional case these limits are smooth Ricci shrinkers and the convergence is in the pointed smooth Cheeger-Gromov sense. As a consequence, limits along the integral curve of $\nabla f$ starting at such a point $q$ split a line. This generalises known results about the geometry of ends of Ricci shrinkers that relied on global curvature bounds. To obtain our results, we extend the $\mathbb{F}$-convergence theory from Bamler and Li-Wang. |
| title | Geometric Structure of Ends of Ricci Shrinkers |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2508.10790 |