https://neckpinch.com/authors/alessandro-bertellotti/New arXiv papers by Alessandro Bertellotti, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2508.10790/arxiv:2508.10790Thu, 14 Aug 2025 00:00:00 GMTAlessandro Bertellotti, Reto Buzano — 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 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 ∇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 F-convergence theory from Bamler and Li-Wang.Ricci solitonsSingularities4-manifoldsScalar curvature https://neckpinch.com/papers/2407.04131/arxiv:2407.04131Thu, 04 Jul 2024 00:00:00 GMTAlessandro Bertellotti, Reto Buzano — We estimate the number of ends of smooth and singular Ricci shrinkers focussing first on general ends and later on asymptotically conical ones. In particular, we obtain a variety of applications to sequences of Ricci shrinkers converging in a weak pointed sense to a possibly singular limit Ricci shrinker, for instance no new conical end can form in the limit.Ricci solitonsWeak & singular flowsBoundaries & non-compact