4 citations · 5 across the 7 of their papers we have counts for
7 papers
Complex harmonic maps and rank 2 higher Teichmüller theory
Christian El Emam, Nathaniel Sagman
We initiate and develop the theory of complex harmonic maps to holomorphic Riemannian symmetric spaces, which we make use of to study complex analytic aspects of higher Teichmüller…
Compatibility of Goldman's symplectic form with the complex structure on the Hitchin component
Christian El Emam, Nathaniel Sagman
We prove that, on the Hitchin component, the Goldman symplectic form and the Labourie-Loftin complex structure are compatible and together determine a (m…
Holomorphic dependence for the Beltrami equation in Sobolev spaces
Christian El Emam, Nathaniel Sagman
We prove that, given a path of Beltrami differentials on that live in and vary holomorphically in the Sobolev space of an open subset $Ω\subset…
A metric uniformization model for the quasi-Fuchsian space
Christian El Emam
We introduce and study a novel uniformization metric model for the quasi-Fuchsian space QF(S) of a closed oriented surface S, defined through a class of C-valued bilinear forms on…
Immersions of surfaces into SL(2,C) and into the space of geodesics of Hyperbolic space
Christian El Emam
This thesis mainly treats two developments of the classical theory of hypersurfaces inside pseudo-Riemannian space forms. The former - a joint work with Francesco Bonsante - consis…
On PSL(2,C) and on the space of geodesics of H^3 as Riemannian holomorphic manifolds
Christian El Emam
We discuss some geometric aspects of PSL(2,C), SL(2,C), and the space G of the geodesics of H^3 equipped with some suitable structures of Riemannian holomorphic manifolds of consta…
On immersions of surfaces into SL(2,C) and geometric consequences
Francesco Bonsante, Christian El Emam
We approach the study of totally real immersions of smooth manifolds into holomorphic Riemannian space forms of constant sectional curvature -1. We introduce a notion of first and…