https://neckpinch.com/authors/ka-fai-li/New arXiv papers by Ka-Fai Li, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1906.04343/arxiv:1906.04343Tue, 11 Jun 2019 00:00:00 GMTAlbert Chau, Huabin Ge, Ka-Fai Li, Liangming Shen — We establish the existence of the K"ahler-Ricci flow on projective varieties with log canonical singularities. This generalizes some of the existence results of Song-Tian in case of projective varieties with klt singularities. We also prove that the normalized K"ahler-Ricci flow will converge to the \ka-Einstein metric with negative Ricci curvature on semi-log canonical models in the sense of currents. Finally we also construct K"ahler-Ricci flow solutions performing divisorial contractions and flips with log canonical singularities.Ricci flowEinstein metricsSingularitiesAnalytic minimal model program https://neckpinch.com/papers/1708.02717/arxiv:1708.02717Wed, 09 Aug 2017 00:00:00 GMTAlbert Chau, Ka-Fai Li, Liangming Shen — Let M be a compact complex manifold with smooth Kähler metric η, and let D be a smooth divisor on M. Let M=M∖ D and let hatω be a Carlson-Griffiths type metric on M. We study complete solutions to Kähler-Ricci flow on M which are comparable to hatω, starting from a smooth initial metric ω₀=η+i∂∂ φ₀ where φ₀∈ C^(∞)(M). When ω₀≥ c hatω on M for some c>0 and φ₀ has zero Lelong number, we construct a smooth solution ω(t) to Kähler-Ricci flow on M× [0, T_([ω₀ ])) where T_([ω₀ ]):= sup \ T: [η] +T (c₁(K_M) + c₁(𝓞_D))∈ 𝓚_M \ so that ω(t)≥ (1/n − 4Kt/c )hatω for all t≤ c/4nK where K is a non-negative upper bound on the bisectional curvatures of hatω (see Theorem 1.2). In particular, we do not assume ω₀ has bounded curvature. If ω₀ has bounded curvature and is asymptotic to hatω in an appropriate sense, we construct a complete bounded curvature solution on M× [0, T_([ω₀ ])) (see Theorem 1.3). These generalize some of the results of Lott-Zhang in [15]. On the other hand if we only assume ω₀≥ c η on M for some c>0 and φ₀ is bounded on M, we construct a smooth solution to Kähler-Ricci on M× [0, T_([ω₀ ])) which is equivalent to hatω for all positive times. This includes as a special case when ω₀ is smooth on M in which case the solution becomes instantaneously complete on M under Kähler-Ricci flow (see Theorem 1.1).Ricci flowKähler–Ricci flowSingularitiesKähler geometry