Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Bertellotti, Alessandro, Buzano, Reto
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979316948
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