41 citations · 72 across the 11 of their papers we have counts for
15 papers
Fine properties of monotone maps arising in optimal transport for non-quadratic costs
Cristian E. Gutierrez, Annamaria Montanari
The cost functions considered are , where , homogeneous of degree , with a positive definite Hessian in the unit sphere. We study mu…
Sobolev inequalities with jointly concave weights on convex cones
Zoltán M. Balogh, Cristian E. Gutiérrez, Alexandru Kristály
Using optimal mass transport arguments, we prove weighted Sobolev inequalities of the form \[\left(\int_E |u(x)|^q\,ω(x) \,dx\right)^{1/q}\leq K_0\,\left(\int_E |\nabla u(x)|^p\,σ(…
-estimates for the near field refractor
Cristian E. Gutierrez, Federico Tournier
We establish local estimates for one source near field refractors under structural assumptions on the target, and with no assumptions on the smoothness of the densities.
Refractors in anisotropic media associated with norms
Cristian E. Gutierrez, Qingbo Huang, Henok Mawi
We show existence of interfaces between two anisotropic materials so that light is refracted in accordance with a given pattern of energy. To do this we formulate a vector Snell la…
Reflection and refraction problems for metasurfaces related to Monge-Ampère equations
Cristian E. Gutierrez, Luca Pallucchini
A metasurface is a surface, tipically a plane, on which a function called phase discontinuity is chosen so that the metasurface produces a desired reflection or refraction job. We…
On the existence of dichromatic single element lenses
Cristian E. Gutierrez, Ahmad Sabra
Due to dispersion, light with different wavelengths, or colors, is refracted at different angles. Our purpose is to determine when is it possible to design a lens made of a single…