4 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…
Local asymptotics for Hitchin's equations and high energy harmonic maps
Nathaniel Sagman, Peter Smillie
We find new estimates and a new asymptotic decoupling phenomenon for solutions to Hitchin's self-duality equations at high energy. These generalize previous results for generically…
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…
A factorization theorem for harmonic maps
Nathaniel Sagman
Let be a harmonic map from a Riemann surface to a Riemannian -manifold. We prove that if there is a holomorphic diffeomorphism between open subsets of the surface such t…