3 papers
math.AP2025
Global regularity for the Dirichlet problem of Monge-Ampère equation in convex polytopes
Genggeng Huang, Weiming Shen
We study the Dirichlet problem for Monge-Ampère equation in bounded convex polytopes. We give sharp conditions for the existence of global and convex solutions prov…
math.AP2024
Monge-Ampère equation with Guillemin boundary condition in high dimension
Genggeng Huang, Weiming Shen
The Guillemin boundary condition naturally appears in the study of Kähler geometry of toric manifolds. In the present paper, the following Guillemin boundary value problem is inves…
math.AP2023
The Monge-Ampère equation in cones and polygonal domains
Genggeng Huang, Weiming Shen
We study asymptotic behaviors of solutions to the Monge-Ampère equation in cones and use the expansion as a tool to study the regularity of solutions in polygonal domains.