Observational analysis reveals existence and uniqueness for the multi-marginal Monge problem in compact metric spaces, indicating potential for advanced metalens applications.
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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Altiner et al. (2025) studied this question.
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