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Solutions to Monge-Ampère Equations with Low Codimensional singularities
Abstract
We construct solutions to Monge-Ampère equations whose Monge-Ampère measures contain singular components supported on low codimensional sets. We also study the regularity of such solutions. To motivate our construction, we present examples arising from optimal transport where the potential of optimal transport maps satisfy Monge-Ampère equations similar to the ones we study.
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BibTeX
@misc{rakshit2026solutions,
title = {{Solutions to Monge-Ampère Equations with Low Codimensional singularities}},
author = {Arghya Rakshit and Aranya Sen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.19142},
eprint = {2605.19142},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.19142},
}
RIS
TY - UNPB
TI - Solutions to Monge-Ampère Equations with Low Codimensional singularities
AU - Arghya Rakshit
AU - Aranya Sen
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2605.19142
UR - https://arxiv.org/abs/2605.19142
AB - We construct solutions to Monge-Ampère equations whose Monge-Ampère measures contain singular components supported on low codimensional sets. We also study the regularity of such solutions. To motivate our construction, we present examples arising from optimal transport where the potential of optimal transport maps satisfy Monge-Ampère equations similar to the ones we study.
ER -