Arghya Rakshit

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20222026

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math.AP2026

Solutions to Monge-Ampère Equations with Low Codimensional singularities

Arghya Rakshit, Aranya Sen

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 s…

math.AP2024

Pointwise Schauder estimates for optimal transport maps of rough densities

Arghya Rakshit

We prove a pointwise $C^{2, α}$ estimate for the potential of the optimal transport map in the case that the densities are only close to constant in a certain $L^{p}$ sense.

math.AP2023

Sobolev regularity for optimal transport maps of non-convex planar domains

Connor Mooney, Arghya Rakshit

We prove a sharp global $W^{2, p}$ estimate for potentials of optimal transport maps that take a certain class of non-convex planar domains to convex ones.

math.AP2022

Singular structures in solutions to the Monge-Ampère equation with point masses

Connor Mooney, Arghya Rakshit

We construct new examples of Monge-Ampère metrics with polyhedral singular structures, motivated by problems related to the optimal transport of point masses and to mirror symmetry…