Li Sheng

activity

20102026

most citedAffine techniques on extremal metrics on toric surfaces

19 citations · 76 across the 22 of their papers we have counts for

collaborators

Showing 2026Show all

4 papers · 1 filter

math.AG2026

K-unstable Toric Varieties and Secondary Polytopes

Chi Li, Li Sheng, Yi Yao

For K-unstable toric varieties, Székelyhidi's optimal test-function $Θ_{P}$ is a mysterious concave function over the moment polytope $P$ , which gives the maximal destabilizer for…

math.AP2026

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 $det (u_{i j ˉ}) = 1$ with homogeneous Dirichlet data under the…

math.AP2026

Power Convexity of Solutions to the Complex Monge-Ampère Equation $det (u_{i j}) = 1$ 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 $det (u_{i j}) = 1$ in a convex set in the complex 2 dimensional Euclidean…

math.AP2026

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 $C^{n}$ . We prove that u itself is strictly convex.

K-unstable Toric Varieties and Secondary Polytopes

Pogorelov interior estimates and a Liouville theorem for the complex Monge--Ampère equation

Power Convexity of Solutions to the Complex Monge-Ampère Equation det(uij​​)=1 in Complex Dimension Two

Convexity of the Potential Function of the Einstein-Kähler Metric on a Convex Domain

Power Convexity of Solutions to the Complex Monge-Ampère Equation $det (u_{i j}) = 1$ in Complex Dimension Two