5 papers
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\subse…
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…
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 Teichmülle…
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…
Complex affine spheres and a Bers theorem for SL(3,C)
Christian El Emam, Nathaniel Sagman
For a closed surface of genus at least , let be the Hitchin component of representations to equipped with the Labourie-Lofti…