Associate Prof. Jian Wangjian and Co-authors Publish Paper in Inventiones Mathematicae

Recently, the paper Finite time singularities of the Kähler–Ricci flow, jointly authored by Associate Prof. Jian Wangjian from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences(AMSS), Academician Tian Gang of Peking University and Professor Jian Song from Rutgers University, USA, has been published online in Inventiones Mathematicae.

This study establishes uniform boundedness results for scalar curvature and distance, generalizing Perelman’s work on the Fano Kähler‑Ricci flow to general finite‑time solutions of the Kähler‑Ricci flow. These boundedness results are obtained through Li‑Yau‑type estimates and Harnack estimates for the weighted Ricci potential function of the Kähler‑Ricci flow, developed by the three authors. The research further proves that, with an appropriate choice of base points, Type‑I blow‑ups of such finite‑time solutions always sub‑converge in the Gromov‑Hausdorff sense to an ancient solution on a family of analytic normal varieties. As a corollary, fibres over every relatively compact open subset of the regular base manifold of this fibration satisfy a Type‑I diameter bound. Using these estimates, the work also demonstrates that all Kähler‑Ricci flows with Calabi symmetry necessarily develop Type‑I singularities, including both high‑codimensional collapsing and fibre collapsing scenarios.

In summary, by developing new estimation tools, this research extends for the first time the boundedness of scalar curvature and distance for Fano Kähler‑Ricci flows to all general finite‑time solutions of the Kähler‑Ricci flow, and characterizes the sub‑convergence limits of Type‑I blow‑ups in the Gromov‑Hausdorff sense. It constitutes an important achievement in geometric analysis. The paper also forms a key component of the Analytic Minimal Model Program proposed by Jian Song and Tian Gang. The preprint of this research was uploaded to arXiv in October 2023, and the article was formally accepted by Inventiones Mathematicae on September 8, 2026.

Associate Prof. Jian Wangjian received his bachelor’s degree from the University of Science and Technology of China in 2014 and his doctorate from Peking University in 2019 under the supervision of Academician Tian Gang. After completing his doctoral studies, he carried out post‑doctoral research at AMSS, with Academician Zhou Xiangyu as his co‑supervisor. He formally joined AMSS in 2021. His research interests lie in geometric analysis and complex geometry, specifically covering the Kähler‑Ricci flow, Ricci flow, collapsed Calabi‑Yau metrics and other related topics. He has achieved a series of outstanding results in the field of the Kähler‑Ricci flow.