4 papers
Harmonic extension of Weil-Petersson circle homeomorphisms
Farid Diaf, Vladimir Marković, Abderrahim Mesbah
In this paper, we study Weil--Petersson circle homeomorphisms from the viewpoint of harmonic maps. We prove that a homeomorphism is Weil--Petersson if…
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…
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…
The Anti-de Sitter proof of Thurston's earthquake theorem
Farid Diaf, Andrea Seppi
Thurston's earthquake theorem asserts that every orientation-preserving homeomorphism of the circle admits an extension to the hyperbolic plane which is a (left or right) earthquak…