Nathaniel Sagman

activity

20202026

most citedUnstable minimal surfaces in symmetric spaces of non-compact type

5 citations · 8 across the 14 of their papers we have counts for

collaborators

17 papers

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 $X$ be a hyperbolic Riemann surface and let $μ$ and $ν$ be laminations on $X$ homotopic to measured foliations with finite Dirichlet integral. We prove that $μ$ and $ν$ 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 $C$ to $R^{n}$ is stable if and only if it lives in an even dimensional affine subspace and is holomorphic for som…

math.DG2025

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…

math.DG2025

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…

math.DG2024

Compatibility of Goldman's symplectic form with the complex structure on the $SL (3, R)$ Hitchin component

Christian El Emam, Nathaniel Sagman

We prove that, on the $SL (3, R)$ Hitchin component, the Goldman symplectic form and the Labourie-Loftin complex structure are compatible and together determine a (m…

math.DG2024

On Hitchin's equations for cyclic G-Higgs bundles

Nathaniel Sagman, Ognjen Tošić

We develop a Lie-theoretic perspective on Hitchin's equations for cyclic $G$ -Higgs bundles, which we use to study analytic and geometric properties of harmonic maps. Among other th…

math.CV2024

Holomorphic dependence for the Beltrami equation in Sobolev spaces

Christian El Emam, Nathaniel Sagman

We prove that, given a path of Beltrami differentials on $C$ that live in and vary holomorphically in the Sobolev space $W_{l oc}^{l, \infty} (Ω)$ of an open subset $Ω\subset…

math.DG2024

Complex affine spheres and a Bers theorem for SL(3,C)

Christian El Emam, Nathaniel Sagman

For $S$ a closed surface of genus at least $2$ , let $Hit_{3} (S)$ be the Hitchin component of representations to $SL (3, R),$ equipped with the Labourie-Lofti…

math.DG2023

Minimal diffeomorphisms with $L^{1}$ Hopf differentials

Nathaniel Sagman

We prove that for any two Riemannian metrics $σ_{1}, σ_{2}$ on the unit disk, a homeomorphism $\partial D \to \partial D$ extends to at most one quasiconformal minimal di…

math.GT2023

Non-convexity of extremal length

Nathaniel Sagman

With respect to every Riemannian metric, the Teichmüller metric, and the Thurston metric on Teichmüller space, we show that there exist measured foliations on surfaces whose extrem…

math.DG2023★ 1 cited

Minimal surfaces and the new main inequality

Vladimir Markovic, Nathaniel Sagman

We establish the new main inequality as a minimizing criterion for minimal maps to products of $R$ -trees, and the infinitesimal new main inequality as a stability criterio…

math.DG2022★ 5 cited

Unstable minimal surfaces in symmetric spaces of non-compact type

Nathaniel Sagman, Peter Smillie

We prove that if $Σ$ is a closed surface of genus at least 3 and $G$ is a split real semisimple Lie group of rank at least $3$ acting faithfully by isometries on a symmetric space…

math.DG2022★ 2 cited

Unstable minimal surfaces in $R^{n}$ and in products of hyperbolic surfaces

Vladimir Markovic, Nathaniel Sagman, Peter Smillie

We prove that every unstable equivariant minimal surface in $R^{n}$ produces a maximal representation of a surface group into $\prod_{i = 1}^{n} PSL (2, R)$ toget…

math.DG2021

Spaces of harmonic surfaces in non-positive curvature

Nathaniel Sagman

Let $M (Σ)$ be an open and connected subset of the space of hyperbolic metrics on a closed orientable surface, and $M (M)$ an open and connected subset of the s…

math.DG2021

Almost strict domination and anti-de Sitter 3-manifolds

Nathaniel Sagman

We define a condition called almost strict domination for pairs of representations $ρ_{1} : π_{1} (S_{g, n}) \to PSL (2, R)$ , $ρ_{2} : π_{1} (S_{g, n}) \to G$ , where $G$ is the isome…

math.DG2020

A factorization theorem for harmonic maps

Nathaniel Sagman

Let $f$ be a harmonic map from a Riemann surface to a Riemannian $n$ -manifold. We prove that if there is a holomorphic diffeomorphism $h$ between open subsets of the surface such t…

Quadratic differentials in Teichmüller theory and complex harmonic maps

Holomorphic realizations of pairs of foliations on Riemann surfaces

Holomorphicity of stable minimal surfaces of low genus

Complex harmonic maps and rank 2 higher Teichmüller theory

Local asymptotics for Hitchin's equations and high energy harmonic maps

Compatibility of Goldman's symplectic form with the complex structure on the SL(3,R) Hitchin component

On Hitchin's equations for cyclic G-Higgs bundles

Holomorphic dependence for the Beltrami equation in Sobolev spaces

Complex affine spheres and a Bers theorem for SL(3,C)

Minimal diffeomorphisms with L1 Hopf differentials

Non-convexity of extremal length

Minimal surfaces and the new main inequality

Unstable minimal surfaces in symmetric spaces of non-compact type

Unstable minimal surfaces in Rn and in products of hyperbolic surfaces

Spaces of harmonic surfaces in non-positive curvature

Almost strict domination and anti-de Sitter 3-manifolds

A factorization theorem for harmonic maps

Compatibility of Goldman's symplectic form with the complex structure on the $SL (3, R)$ Hitchin component

Minimal diffeomorphisms with $L^{1}$ Hopf differentials

Unstable minimal surfaces in $R^{n}$ and in products of hyperbolic surfaces