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math.DG2026
Quadratic differentials in Teichmüller theory and complex harmonic maps
Christian El Emam, Nathaniel Sagman
We show that Hitchin-Wolf's harmonic map parametrization of Teichmüller space, the Schwarzian holonomy map, and Uhlenbeck's almost-Fuchsian holonomy map all arise as restrictions o…
math.GT2026
Holomorphic realizations of pairs of foliations on Riemann surfaces
Nathaniel Sagman, Dragomir Saric
Let be a hyperbolic Riemann surface and let and be laminations on homotopic to measured foliations with finite Dirichlet integral. We prove that and are fil…
math.DG2026
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…