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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 -Higgs bundles, which we use to study analytic and geometric properties of harmonic maps. Among other th…
math.DG2024
Constant energy families of harmonic maps
Ognjen Tošić
For a negatively curved manifold and a continuous map from a closed surface , we study complex submanifolds of Teichmüller space $\mathcal{S}\subset\mathcal{T}(Σ)…
math.DG2022
Harmonic projections in negative curvature
Ognjen Tošić
In this paper we construct harmonic maps that are at a bounded distance from nearest-point retractions to convex sets, in negatively curved manifolds. Specifically, given a quasidi…