7 papers · 1 filter
The inverse curve shortening flow on the hyperbolic plane
Ivan KrznariÄ, Rafael López
We study the inverse curve shortening flow in the hyperbolic plane $\h^2$. We classify all solitons with respect to parabolic and conformal vector fields of $\h^2$. In the upper ha…
Classification of the ruled surfaces that are critical points of the Dirichlet energy
Rafael López
We classify all ruled surfaces in Euclidean space that are critical points of the Dirichlet energy, obtaining explicit parametrizations of these surfaces.
A necessary condition for cylindrical curves in terms of curvature and torsion
Rafael López
We establish necessary conditions for a regular curve to lie on a circular cylinder in terms of its curvature and torsion . By identifying a fundamental function $Ï= \sin…
Homothetical surfaces with constant mean curvature in hyperbolic space
Rafael Belli, Rafael López
We classify all homothetical surfaces with constant mean curvature in the hyperbolic space . Using the upper half-space model with standard coordinates ,…
Circles-foliated stationary surfaces of the Dirichlet energy
Rafael López
In Euclidean space we study surfaces with constant anisotropic mean curvature of the Dirichlet energy . We prove the existence of non-rotational surfaces…
A Characterization of Curves that Lie on a Totally Umbilical Surface of a Space Form
Rafael López
We give necessary and sufficient conditions on the curvature and the torsion of a regular curve of the space forms $\h^3$ and $\s^3$ to be contained in a totally umbilical surface.…