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Research Article | Open Access

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

Connor Mooney( ), Arghya Rakshit
Department of Mathematics, UC Irvine, Irvine, CA 92697-3875, USA
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Abstract

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. We also analyze the stability of the singular structures under small perturbations of the data given in the problem under consideration.

Keywords

Monge-Ampère equationoptimal transportSYZ conjectureregularity and stabilitysingular solutions

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Mathematics in Engineering
Volume 5 Issue 5,
October 2023
Pages 1-11
DOI: 10.3934/mine.2023083

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Cite this article:
Mooney C, Rakshit A. Singular structures in solutions to the Monge-Ampère equation with point masses. Mathematics in Engineering, 2023, 5(5): 1-11. https://doi.org/10.3934/mine.2023083

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Received: 29 April 2022
Revised: 23 October 2022
Accepted: 23 October 2022
Published: 15 October 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)