2025/10/08 by Chen, Longteng
Mathematics · Physics and Astronomy · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.2510.06850
In this work, we consider a perturbation of an asymptotically conical gradient expanding Kähler-Ricci soliton metric g in the same Kähler class. We demonstrate that, under suitable assumptions, the normalized Kähler-Ricci flow starting from the initial perturbed metric exists for all time and converges uniformly to an asymptotically conical gradient expanding Kähler-Ricci soliton metric g_∞. Moreover, if the perturbed initial metric is asymptotic to g at spatial infinity, then the limiting metric coincides with the original soliton, that is, g_∞ = g.