https://neckpinch.com/authors/bruce-kleiner/New arXiv papers by Bruce Kleiner, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2312.02106arxiv:2312.02106Mon, 04 Dec 2023 00:00:00 GMTRichard H Bamler, Bruce Kleiner — We prove the Multiplicity One Conjecture for mean curvature flows of surfaces in ℝ³. Specifically, we show that any blow-up limit of such mean curvature flows has multiplicity one. This has several applications. First, combining our work with results of Brendle and Choi-Haslhofer-Hershkovits-White, we show that any level set flow starting from an embedded surface diffeomorphic to a 2-spheres does not fatten. In fact, we obtain that the problem of evolving embedded 2-spheres via the mean curvature flow equation is well-posed within a natural class of singular solutions. Second, we use our result to remove an additional condition in recent work of Chodosh-Choi-Mantoulidis-Schulze. This shows that mean curvature flows starting from any generic embedded surface only incur cylindrical or spherical singularities. Third, our approach offers a new regularity theory for solutions of mean curvature flows that flow through singularities. Among other things, this theory also applies to the innermost and outermost flow of any embedded surface and shows that all singularity models of such flows must have multiplicity one. It also establishes equality of the fattening time with the discrepancy time. Lastly, we obtain a number of further results characterizing a separation phenomenon of mean curvature flows of surfaces.Mean curvature flowSingularitiesWeak & singular flows https://arxiv.org/abs/1709.04122arxiv:1709.04122Wed, 13 Sep 2017 00:00:00 GMTRichard H. Bamler, Bruce Kleiner — We verify a conjecture of Perelman, which states that there exists a canonical Ricci flow through singularities starting from an arbitrary compact Riemannian 3-manifold. Our main result is a uniqueness theorem for such flows, which, together with an earlier existence theorem of Lott and the second named author, implies Perelman's conjecture. We also show that this flow through singularities depends continuously on its initial condition and that it may be obtained as a limit of Ricci flows with surgery. Our results have applications to the study of diffeomorphism groups of three manifolds — in particular to the Generalized Smale Conjecture — which will appear in a subsequent paper.Ricci flowSingularitiesSurgery3-manifoldsSmale conjecture & diffeomorphismsStability & uniqueness https://arxiv.org/abs/1408.2271arxiv:1408.2271Sun, 10 Aug 2014 00:00:00 GMTBruce Kleiner, John Lott — We introduce singular Ricci flows, which are Ricci flow spacetimes subject to certain asymptotic conditions. We consider the behavior of Ricci flow with surgery starting from a fixed initial compact Riemannian 3-manifold, as the surgery parameter varies. We prove that the flow with surgery subconverges to a singular Ricci flow as the surgery parameter tends to zero. We establish a number of geometric and analytical properties of singular Ricci flows.Ricci flowSurgery3-manifoldsWeak & singular flows https://arxiv.org/abs/math/0605667arxiv:math/0605667Thu, 25 May 2006 00:00:00 GMTBruce Kleiner, John Lott — These are detailed notes on Perelman's papers "The entropy formula for the Ricci flow and its geometric applications" and "Ricci flow with surgery on three-manifolds".Ricci flowSurgery3-manifolds