Work

Monge–Ampère Equation With Guillemin Boundary Condition in High Dimension

Year: 2026

Type: article

Abstract: ABSTRACT 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 investigated: , where and is a simple convex polytope in . The solvability of this problem is given under the necessary and sufficient condition. The key issue in the proof is to obtain the boundary regularity of . Due to the difficulty caused by the structure of the equation itself and the singularity of , special attention is required to understand the influence of different singularity types at various positions on and how these impact the behavior of in its vicinity.

Source: Communications on Pure and Applied Mathematics

DOI: 10.1002/cpa.70033

Authors: Genggeng Huang, Weiming Shen

Institutions: Fudan University, Capital Normal University

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Natural Science Foundation of China, National Key Research and Development Program of China

Awards: G3286681150, G5491100983, G7938319195, G8917023756