119 citations · 119 across the 5 of their papers we have counts for
8 papers
-estimates in optimal transport for non quadratic costs
Cristian E. Gutiérrez, Annamaria Montanari
For cost functions with homogeneous of degree , we show -estimates of on balls, where is an -monotone map. Estimates for…
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…
Chromatic Aberration in Metalenses
Cristian E. Gutiérrez, Ahmad Sabra
This paper provides a mathematical approach to study chromatic aberration in metalenses. It is shown that radiation of a given wavelength is refracted according to a generalized Sn…
On the Numerical Solution of the Near Field Refractor Problem
Cristian E. Gutiérrez, Henok Mawi
A numerical scheme is presented to solve the one source near field refractor problem to arbitrary precision and it is proved that the scheme terminates in a finite number of iterat…
Tunable Graphene Metasurface Reflectarray for Cloaking, Illusion and Focusing
Sudipta Romen Biswas, Cristian E Gutiérrez, Andrei Nemilentsau +4
We present a graphene-based metasurface that can be actively tuned between different regimes of operation, such as anomalous beam steering and focusing, cloaking and illusion optic…
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…
On the Numerical Solution of the Far Field Refractor Problem
Roberto De Leo, Cristian E. Gutiérrez, Henok Mawi
The far field refractor problem with a discrete target is solved with a numerical scheme that uses and simplify ideas from Caffarelli, Kochengin and Oliker. A numerical implementat…
Interior second derivative estimates for solutions to the linearized Monge--Ampère equation
Cristian E. Gutiérrez, Truyen Nguyen
Let be a bounded convex domain and be a convex function such that is sufficiently smooth on and the Monge--Ampère measure $\det D^2ϕ…