English

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

R2 v1 2026-06-24T10:57:13.925Z