https://neckpinch.com/authors/hosea-wondo/New arXiv papers by Hosea Wondo, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2509.20669arxiv:2509.20669Thu, 25 Sep 2025 00:00:00 GMTXiaodong Cao, Ernani Ribeiro, Hosea Wondo — We investigate four-dimensional gradient shrinking Ricci solitons with positive modified sectional curvature. Our first main result shows that if the norm of the self-dual Weyl tensor and the scalar curvature satisfy a certain sharp pinching condition (closely related, in a precise sense, to that of Kähler metric), then the soliton is necessarily locally Kähler. We further obtain a characterization theorem and a weighted integral gap result for compact gradient shrinking Ricci solitons with bounded modified sectional curvature. In addition, we establish a Hitchin-Thorpe type inequality for compact four-dimensional Ricci solitons, providing new topological constraints on such manifolds.Ricci solitonsCurvature pinching4-manifoldsKähler geometryScalar curvature https://arxiv.org/abs/2408.12797arxiv:2408.12797Fri, 23 Aug 2024 00:00:00 GMTHosea Wondo — We extend some results known for the Kähler-Ricci flow to the Chern-Ricci flow regarding the independence of singularity types for long-time solutions. Specifically, we show that if a solution to the Chern-Ricci flow exists with uniformly bounded torsion and curvature, then any other solution starting from an initial metric of the same ∂∂ class will also exhibit uniform bounds on torsion and curvature.Ricci flowKähler–Ricci flowGeneralized & G₂ flowsSingularitiesKähler geometryLong-time existence & convergence https://arxiv.org/abs/2308.12527arxiv:2308.12527Thu, 24 Aug 2023 00:00:00 GMTHosea Wondo, Zhou Zhang — In this paper, we show that the singularity type of solutions to the Käher-Ricci flow on a numerically effective manifold does not depend on the initial metric. More precisely if there exists a type III solution to the Kähler-Ricci flow, then any other solution starting from a different initial metric will also be Type III. This generalises previous results by Y. Zhang for the semi-ample case.Ricci flowKähler–Ricci flowSingularitiesKähler geometryLong-time existence & convergenceAnalytic minimal model programNumerics & visualization https://arxiv.org/abs/2210.04546arxiv:2210.04546Mon, 10 Oct 2022 00:00:00 GMTHosea Wondo — We study the convergence and curvature blow up of La Nave and Tian's continuity method on a generalised Hirzebruch surface. We show that the Gromov-Hausdorff convergence is similar to that of the Kahler-Ricci flow and obtain curvature estimates. We also show that a general solution to the continuity method either exist or all times, or the scalar curvature blows up. This behavior is known to be exhibited by the Kahler-Ricci flow.Ricci flowKähler–Ricci flowSingularitiesKähler geometryScalar curvatureLimit spaces & RCD https://arxiv.org/abs/2111.06615arxiv:2111.06615Fri, 12 Nov 2021 00:00:00 GMTHosea Wondo — We obtain curvature estimates for long time solutions of the continuity method on compact Kähler manifolds with semi-ample canonical line bundles. In this setting, initiated in arXiv:1410.3157 and arXiv:0709.0990, we adapt arguments from arXiv:1903.05939 for the Kähler-Ricci flow to this setup. As an application, we derive curvature bounds for general metrics on product manifolds.Ricci flowKähler–Ricci flowKähler geometryLong-time existence & convergenceAnalytic minimal model program