https://neckpinch.com/authors/jiyuan-han/New arXiv papers by Jiyuan Han, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2610.01202/arxiv:2610.01202Thu, 01 Oct 2026 00:00:00 GMTJiyuan Han — We prove a uniform L^∞-estimate for the parabolic Monge–Ampère equation under uniform Hörmander-Tian type estimates with respect to the initial and prescribed measures. We apply this estimate to rescaled Kähler–Ricci flows on a family of polarized Calabi–Yau manifolds over the punctured disk. An interpolation argument gives uniform Hörmander-Tian type estimates along the flows. We also establish uniform diameter bounds and Gromov–Hausdorff precompactness for this family of flows. In particular, we obtain an alternative proof of the diameter estimate by Li-Tosatti.Ricci flowKähler–Ricci flowRicci-flat & Calabi–YauKähler geometryLimit spaces & RCD https://neckpinch.com/papers/2406.10939/arxiv:2406.10939Sun, 16 Jun 2024 00:00:00 GMTJiyuan Han, Yaxiong Liu — In this paper, we prove that on a smooth Kähler manifold, the G-coercivity of the weighted Mabuchi functional implies the existence of the (v, w)-weighted-cscK (extremal) metric with v log-concave (firstly studied in), e.g, cscK metrics, Kähler-Ricci solitons, μ-cscK metrics.Ricci solitonsKähler–Ricci solitonsKähler geometryKähler–Einstein & K-stability