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

2023/09/26 by Jonsson, Mattias, McCleerey, Nicholas, Patram, Neil +1 · 1 citation
#49Q22 (Secondary) #53B05 (Primary) 35J96 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.15263

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 S² near each of the 6 singular points. We deduce in addition that the solution is not 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.

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