Work

Singularities of the solution to a Monge–Ampère equation on the boundary of the 3-simplex

Year: 2025

Type: article

Abstract: We show that the metric defined by the solution to the tropical Monge–Ampère equation, as defined by Hultgren, Mazzon, and the first two authors, on the boundary of the 3-simplex is asymptotic to the Gross–Wilson metric on $$S^2$$ S 2 near each of the 6 singular points. We deduce in addition that the solution is not $$C^{1,1}$$ C 1 , 1 across the singular points. Compared to previous works, our starting point is the real Monge–Ampère equation, as opposed to the complex structure.

Source: Journal of Geometric Analysis

DOI: 10.1007/s12220-025-02199-7

Authors: Mattias Jonsson, Nicholas McCleerey, Neil Patram, Benjamin W. Scott

Institutions: University of Michigan, Purdue University West Lafayette, Georgia Institute of Technology, Princeton University

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: National Science Foundation