Singular structures in solutions to the Monge-Amp\`{e}re equation with point masses
Analysis of PDEs
2022-04-26 v1
Abstract
We construct new examples of Monge-Amp\`{e}re metrics with polyhedral singular structures, motivated by problems related to the optimal transport of point masses and to mirror symmetry. We also analyze the stability of the singular structures under small perturbations of the data given in the problem under consideration.
Keywords
Cite
@article{arxiv.2204.11365,
title = {Singular structures in solutions to the Monge-Amp\`{e}re equation with point masses},
author = {Connor Mooney and Arghya Rakshit},
journal= {arXiv preprint arXiv:2204.11365},
year = {2022}
}
Comments
10 pages