arXiv subjects

Hosea Wondo

Publications and source records attributed to Hosea Wondo.

5 recordsLinked to original sources

arXiv2025

Gradient Shrinking Ricci Solitons and Modified Sectional Curvature

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 K\"ahler metric), then the soliton is necessarily locally K\"ahler. 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.

math.DG↗

arXiv2024

Singularity Types for Long-Time Chern-Ricci Flow

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 $\partial \bar{\partial}$ class will also exhibit uniform bounds on torsion and curvature.

math.DG↗

arXiv2023

Independence of Singularity Type for Numerically Effective Kähler-Ricci Flows

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.

math.DG↗

arXiv2022

Calabi Symmetry and the Continuity Method

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.

math.DG↗

arXiv2022

Curvature Estimates for the Continuity Method

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.

math.DG↗