8 papers
Holomorphicity of stable minimal surfaces of low genus
Nathaniel Sagman, Thomas-René Thalmaier
We prove that a (branched) minimal immersion from to is stable if and only if it lives in an even dimensional affine subspace and is holomorphic for som…
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…
On Hitchin's equations for cyclic G-Higgs bundles
Nathaniel Sagman, Ognjen ToÅ¡iÄ
We develop a Lie-theoretic perspective on Hitchin's equations for cyclic -Higgs bundles, which we use to study analytic and geometric properties of harmonic maps. Among other th…
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…
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…