Singularities of the solution to a Monge--Amp\`ere equation on the boundary of the 3-simplex
| Autor: | Jonsson, Mattias, McCleerey, Nicholas, Patram, Neil, Scott, Benjamin W. |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 16 pages, 4 figures. Comments welcome! |
| Databáze: | arXiv |
| Externí odkaz: |
|