The Multi-marginal Monge Problem and an application to metasurfaces

Abstract This paper studies the multi-marginal Monge problem in the setting of compact metric spaces proving existence and uniqueness of solutions when the cost function is Lipschitz. We apply the results obtained to solve an optics problem involving metalenses, that is, we design a refracting-reflecting metalens that preserves given energy distributions.

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Publication Details

Journal
Calculus of Variations and Partial Differential Equations
Published
2026-04-21
DOI
https://doi.org/10.1007/s00526-026-03332-2
Primary Topic
Geometry and complex manifolds
Type
article
Field-Weighted Citation Impact
0.00
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article

The Multi-marginal Monge Problem and an application to metasurfaces

Cristian E. Gutiérrez, Irem Altiner
Calculus of Variations and Partial Differential Equations
Geometry and complex manifolds
article

The Multi-marginal Monge Problem and an application to metasurfaces

Cristian E. Gutiérrez, Irem Altiner
article en

Abstract

Abstract This paper studies the multi-marginal Monge problem in the setting of compact metric spaces proving existence and uniqueness of solutions when the cost function is Lipschitz. We apply the results obtained to solve an optics problem involving metalenses, that is, we design a refracting-reflecting metalens that preserves given energy distributions.

Calculus of Variations and Partial Differential EquationsVol. 65(5)
Arizona State University (US), Temple University (US)
Openalex Percentile: Top 96%
Geometry and complex manifolds
DOIOpen Access PDFOpenAlex
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The Multi-marginal Monge Problem and an application to metasurfaces — Cristian E. Gutiérrez, Irem Altiner · Calculus of Variations and Partial Differential Equations (2026) | TGRS Research Map | TGRS