https://neckpinch.com/authors/andrew-d-mcleod/New arXiv papers by Andrew D. McLeod, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1906.07292/arxiv:1906.07292Mon, 17 Jun 2019 00:00:00 GMTAndrew D. McLeod, Peter M. Topping — In this paper, we construct a pyramid Ricci flow starting with a complete Riemannian manifold (Mⁿ,g₀) that is PIC1, or more generally satisfies a lower curvature bound K_(IC₁)≥ −α₀. That is, instead of constructing a flow on M× [0,T], we construct it on a subset of space-time that is a union of parabolic cylinders B_(g₀)(x₀,k)× [0,Tₖ] for each natural number k, where Tₖdownarrow 0, and prove estimates on the curvature and Riemannian distance. More generally, we construct a pyramid Ricci flow starting with any noncollapsed IC₁-limit space, and use it to establish that such limit spaces are globally homeomorphic to smooth manifolds via homeomorphisms that are locally bi-Hölder.Ricci flow(Non)collapsingSphere theorems https://neckpinch.com/papers/1807.09005/arxiv:1807.09005Tue, 24 Jul 2018 00:00:00 GMTAndrew D. McLeod — We obtain an improved pseudolocality result for Ricci flows on two-dimensional surfaces that are initially almost-hyperbolic on large hyperbolic balls. We prove that, at the central point of the hyperbolic ball, the Gauss curvature remains close to the hyperbolic value for a time that grows exponentially in the radius of the ball. This two-dimensional result allows us to precisely conjecture how the phenomenon should appear in the higher dimensional setting.Ricci flowSurfaces https://neckpinch.com/papers/1803.00414/arxiv:1803.00414Thu, 01 Mar 2018 00:00:00 GMTAndrew D. McLeod, Peter M. Topping — We construct a global homeomorphism from any 3D Ricci limit space to a smooth manifold, that is locally bi-Holder. This extends the recent work of Miles Simon and the second author, and we build upon their techniques. A key step in our proof is the construction of local "pyramid Ricci flows", existing on uniform regions of spacetime, that are inspired by Hochard's partial Ricci flows.Ricci flow3-manifoldsLimit spaces & RCD