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arXiv · 2309.15263

Singularities of the solution to a Monge--Amp\`ere equation on the boundary of the 3-simplex

Mattias Jonsson·Nicholas McCleerey·Neil Patram·Benjamin W. Scott
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Abstract

We show that the metric defined by the solution to the tropical Monge-Amp\`ere 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 $S^2$ 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-Amp\`ere equation, as opposed to the complex structure.

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Mattias Jonsson, Nicholas McCleerey, Neil Patram, Benjamin W. Scott. 2023-09-26. Singularities of the solution to a Monge--Amp\`ere equation on the boundary of the 3-simplex. https://arxiv.org/abs/2309.15263

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