Cristian E. Guti'errez

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20122021

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math.AP2021

$L^{\infty}$ -estimates in optimal transport for non quadratic costs

Cristian E. Gutiérrez, Annamaria Montanari

For cost functions $c (x, y) = h (x - y)$ with $h \in C^{2}$ homogeneous of degree $p \geq 2$ , we show $L^{\infty}$ -estimates of $T x - x$ on balls, where $T$ is an $h$ -monotone map. Estimates for…

math.AP2021

Metasurfaces and Optimal transport

Cristian E. Gutiérrez, Qingbo Huang, Quentin Mérigot +1

This paper provides a theoretical and numerical approach to show existence, uniqueness, and the numerical determination of metalenses refracting radiation with energy patterns. The…

math.AP2017

Harnack's inequality for a class of non-divergent equations in the Heisenberg group

Farhan Abedin, Cristian E. Gutiérrez, Giulio Tralli

We prove an invariant Harnack's inequality for operators in non-divergence form structured on Heisenberg vector fields when the coefficient matrix is uniformly positive definite, c…

math.AP2012

Interior second derivative estimates for solutions to the linearized Monge--Ampère equation

Cristian E. Gutiérrez, Truyen Nguyen

Let $Ω \subset R^{n}$ be a bounded convex domain and $ϕ \in C (Ω ˉ)$ be a convex function such that $ϕ$ is sufficiently smooth on $\partial Ω$ and the Monge--Ampère measure $\det D^2ϕ…

L∞-estimates in optimal transport for non quadratic costs

Metasurfaces and Optimal transport

Harnack's inequality for a class of non-divergent equations in the Heisenberg group

Interior second derivative estimates for solutions to the linearized Monge--Ampère equation

$L^{\infty}$ -estimates in optimal transport for non quadratic costs