4 papers
math.DG2023
Catenaries in Riemannian Surfaces
Luiz C. B. da Silva, Rafael López
The concept of catenary has been recently extended to the sphere and the hyperbolic plane by the second author [López, arXiv:2208.13694]. In this work, we define catenaries on any…
math.DG2023
Compact surfaces with boundary with prescribed mean curvature depending on the Gauss map
Antonio Bueno, Rafael López
Given a function defined in the unit sphere , an -surface is a surface in the Euclidean space whose mean curvature…
math.DG2023
The Plateau-Rayleigh instability of translating -solitons
Antonio Bueno, Rafael López, Irene Ortiz
Given a unit vector and , a translating -soliton is a surface in whose mean curvature satisfies $H=\langle N,\text…
math.DG2022
The hanging chain problem in the sphere and in the hyperbolic plane
Rafael López
In this paper, the notion of the catenary curve in the sphere and in the hyperbolic plane is introduced. In both spaces, a catenary is defined as the shape of a hanging chain when…