https://neckpinch.com/authors/gregory-edwards/New arXiv papers by Gregory Edwards, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1905.13114/arxiv:1905.13114Thu, 30 May 2019 00:00:00 GMTGregory Edwards — The Hopf surfaces provide a family of minimal non-Kähler surfaces of class VII on which little is known about the Chern-Ricci flow. We use a construction of Gauduchon-Ornea for locally conformally Kähler metrics on primary Hopf surfaces of class 1 to study solutions of the Chern-Ricci flow. These solutions reach a volume collapsing singularity in finite time, and we show that the metric tensor satisfies a uniform upper bound, supporting the conjecture that the Gromov-Hausdorff limit is isometric to a round S¹. Uniform C^(1+β) estimates are also established for the potential. Previous results had only been known for the simplest examples of Hopf surfaces.Ricci flowGeneralized & G₂ flowsSingularities(Non)collapsingKähler geometryLimit spaces & RCD https://neckpinch.com/papers/1704.00360/arxiv:1704.00360Sun, 02 Apr 2017 00:00:00 GMTGregory Edwards — We use the momentum construction of Calabi to study the conical Kähler-Ricci flow on Hirzebruch surfaces with cone angle along the exceptional curve, and show that either the flow Gromov-Hausdorff converges to the Riemann sphere or a single point in finite time, or the flow contracts the cone divisor to a single point and Gromov-Hausdorff converges to a two dimensional projective orbifold. This gives the first example of the conical Kähler-Ricci flow contracting the cone divisor to a single point. At the end, we introduce a conjectural picture of the geometry of finite time non-collapsing singularities of the flow on Kähler surfaces in general.Ricci flowKähler–Ricci flowSingularities(Non)collapsingSurfacesKähler geometryLimit spaces & RCD