Alexander Murcia — Neckpinchhttps://neckpinch.com/authors/alexander-murcia/New arXiv papers by Alexander Murcia, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT On the rate of convergence of the p-curve shortening flowhttps://neckpinch.com/papers/1702.06983/arxiv:1702.06983Wed, 22 Feb 2017 00:00:00 GMTJean C. Cortissoz, Andrés Galindo, Alexander Murcia — In this paper we give rates of convergence for the p-curve shortening flow for p≥ 1 an integer, which improves on the known estimates and which are probably sharp.Curve shortening The Ricci flow on a cylinderhttps://neckpinch.com/papers/1604.02132/arxiv:1604.02132Thu, 07 Apr 2016 00:00:00 GMTJean Cortissoz, Alexander Murcia — In this paper we study the Ricci flow on surfaces homeomorphic to a cylinder (that is, a product of the circle with a compact interval). We prove longtime existence results, results on the asymptotic behavior of the flow, and we report on an interesting phenomenon: convergence to constant curvature in the normalised flow,under certain assumptions on the initial data, cannot be exponential.Ricci flowSurfacesLong-time existence & convergence