13 citations · 37 across the 11 of their papers we have counts for
11 papers
The Partial -estimate along a general continuity path and applications
Ke Feng, Liangming Shen
We establish a new partial -estimate along a continuity path mixed with conic singularities along a simple normal crossing divisor and a positive twisted -form on Fan…
The K"ahler-Ricci flow with Log Canonical Singularities
Albert Chau, Huabin Ge, Ka-Fai Li +1
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 \cite{ST3…
On the deformation of ball packings
Huabin Ge, Wenshuai Jiang, Liangming Shen
In this paper, we study the geometric aspects of ball packings on , where is a triangulation on a 3-manifold . We introduce a combinatorial Yamabe…
The Kähler-Ricci flow on pseudoconvex domains
Huabin Ge, Aijin Lin, Liangming Shen
We establish the existence of Kähler-Ricci flow on pseudoconvex domains with general initial metric without curvature bounds. Moreover we prove that this flow is simultaneously com…
Gradient flow of the norm squared of a moment map over Kahler manifolds
Aijin Lin, Liangming Shen
Inspired by Wilkin's work [23, 24] on Morse theory for the moduli space of Higgs bundles, we study the moduli space of gauged holomorphic maps by a heat flow approach in the spirit…
Kähler-Ricci flow of cusp singularities on quasi projective varieties
Albert Chau, Ka-Fai Li, Liangming Shen
Let be a compact complex manifold with smooth Kähler metric , and let be a smooth divisor on . Let and let b…
Conic Kähler-Einstein metrics along simple normal crossing divisors on Fano manifolds
Aijin Lin, Liangming Shen
We prove that on one Kähler-Einstein Fano manifold without holomorphic vector fields, there exists a unique conical Kähler-Einstein metric along a simple normal crossing divisor wi…
Smoothing conic Kähler metrics with uniformly upper bisectional curvature bound
Liangming Shen
Based on C. Li and Y. Rubinstein's upper bisectional curvature bound estimate for the conic Kähler metric, we can construct a smoothing sequence for the conic metric with uniformly…
-estimate for conical Kähler-Ricci flow
Liangming Shen
We establish a parabolic version of Tian's -estimate for conical complex Monge-Ampere equations, which includes conical Kähler-Einstein metrics. Our estimate will complete…
Unnormalize conical Kähler-Ricci flow
Liangming Shen
We generalize the maximal time existence of Kähler-Ricci flow in Tian-Zhang and Song-Tian to conical case. Furthermore, if the twisted canonical bundle is big or b…
Smooth approximation of conic Kähler metric with lower Ricci curvature bound
Liangming Shen
We apply Tian's method in Kahler-Einstein problem to prove that a conic K\''ahler metric with lower Ricci curvature bound can be approximated by smooth K\''ahler metrics with the s…