3 papers
math.DG2024
Mean surfaces in Half-Pipe space and infinitesimal Teichmüller theory
Farid Diaf
We study a correspondence between smooth spacelike surfaces in Half-Pipe space and divergence-free vector fields on the hyperbolic plane . We show tha…
math.GT2023
The infinitesimal earthquake theorem for vector fields on the circle
Farid Diaf
We prove that any continuous vector field on a circle is the extension in a suitable sense, of a unique infinitesimal earthquake of the hyperbolic plane. Furthermore, we obtain oth…
math.GT2023
Transition of convex core doubles from hyperbolic to Anti-de sitter geometry
Farid Diaf
Let be a surface of negative Euler characteristic, homeomorphic to a closed surface, possibly with a finite number of points removed. In this paper, we present a construction m…