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arXiv · 2605.19142

Solutions to Monge-Amp\`ere Equations with Low Codimensional singularities

Arghya Rakshit·Aranya Sen
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Abstract

We construct solutions to Monge-Amp\`ere equations whose Monge-Amp\`ere 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-Amp\`ere equations similar to the ones we study.

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Arghya Rakshit, Aranya Sen. 2026-05-18. Solutions to Monge-Amp\`ere Equations with Low Codimensional singularities. https://arxiv.org/abs/2605.19142

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