19 citations · 76 across the 22 of their papers we have counts for
25 papers
K-unstable Toric Varieties and Secondary Polytopes
Chi Li, Li Sheng, Yi Yao
For K-unstable toric varieties, Székelyhidi's optimal test-function is a mysterious concave function over the moment polytope , which gives the maximal destabilizer for…
Pogorelov interior estimates and a Liouville theorem for the complex Monge--Ampère equation
Hongyu Chen, Jingchen Hu, Li Sheng
We prove a Pogorelov interior estimate for strictly plurisubharmonic solutions of the complex Monge-Ampère equation with homogeneous Dirichlet data under the…
Power Convexity of Solutions to the Complex Monge-Ampère Equation in Complex Dimension Two
Hongyu Chen, Jingchen Hu, Li Sheng
In this paper, we establish the power convexity of solutions to the complex Monge-Ampère equation in a convex set in the complex 2 dimensional Euclidean…
Convexity of the Potential Function of the Einstein-Kähler Metric on a Convex Domain
Jingchen Hu, Li Sheng
Suppose that u is the potential function of a complete Kähler-Einstein metric on a bounded strictly convex domain in . We prove that u itself is strictly convex.
Extremal metrics on toric manifolds and homogeneous toric bundles
An-Min Li, Zhao Lian, Li Sheng
In this paper, we prove the Yau-Tian-Donaldson conjecture of the filtration version for toric manifolds and homogeneous toric bundles.
A Liouville Theorem on the PDE
An-Min Li, Li Sheng
Let be a smooth plurisubharmonic function which solves $$ \det(f_{i\bar j})=1\;\;\;\;\;\;\mbox{in }Ω\subset \mathbb C^n.$$ Suppose that the metric $ω_{f}=\sqrt{-1}f_{i\bar j}dz…