A. Mart'inez

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20162020

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math.DG2020

Mean convex properly embedded $[φ, e_{3}]$ -minimal surfaces in $R^{3}$

Antonio Martínez, A. L. Martínez-Triviño, J. P. dos Santos

We establish curvature estimates and a convexity result for mean convex properly embedded $[φ, e_{3}]$ -minimal surfaces in $R^{3}$ , i.e., $φ$ -minimal surfaces when $φ$ …

math.DG2019

Equilibrium of Surfaces in a Vertical Force Field

Antonio Martínez, A. L. Martínez-Triviño

In this paper we study $φ$ -minimal surfaces in $R^{3}$ when the function $φ$ is invariant under a two-parametric group of translations. Particularly those which are complete…

math.DG2019

A Calabi's Type Correspondence

Antonio Martínez, A. L. Martínez Triviño

Calabi observed that there is a natural correspondence between the solutions of the minimal surface equation in $R^{3}$ with those of the maximal spacelike surface equation…

math.DG2018

Improper affine spheres and the Hessian one equation

Antonio Martínez, Francisco Milán

Improper affine spheres have played an important role in the development of geometric methods for the study of the Hessian one equation. Here, we review most of the advances we hav…

Mean convex properly embedded [φ,e3​]-minimal surfaces in R3

Equilibrium of Surfaces in a Vertical Force Field

A Calabi's Type Correspondence

Improper affine spheres and the Hessian one equation

Mean convex properly embedded $[φ, e_{3}]$ -minimal surfaces in $R^{3}$