Abderrahim Mesbah

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math.DG2026

Embedded convex surfaces in hyperbolic and anti-de Sitter spaces

Abderrahim Mesbah

We show that given a quasi-circle $C \subset \partial_{\infty} H^{3}$ (respectively $C \subset \partial_{\infty} AD S^{3}$ ) and a complete conformal metr…

math.DG2026

Harmonic extension of Weil-Petersson circle homeomorphisms

Farid Diaf, Vladimir MarkoviÄ, Abderrahim Mesbah

In this paper, we study Weil--Petersson circle homeomorphisms from the viewpoint of harmonic maps. We prove that a homeomorphism $I ¨ : S^{1} \to S^{1}$ is Weil--Petersson i…

math.DG2025

Domination between non-Fuchsian representations and anti-de Sitter geometry

Farid Diaf, Abderrahim Mesbah, Nathaniel Sagman

Motivated by work of various authors on domination between surface group representations, harmonic maps, and $3$ -dimensional anti-de Sitter geometry, we study a new domination prob…

math.DG2025

The Prescribed Metric on Convex Subsets of Anti-de Sitter Space with Quasi-Circle Ideal Boundaries

Abderrahim Mesbah

Let $h^{+}$ and $h^{-}$ be two complete, conformal metrics on the disc $D$ . Assume moreover that the derivatives of the conformal factors of the metrics $h^{+}$ and $h^{-}…