Ognjen Tovsi'c

collaborators

4 papers

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.AG2024

Derivative of the Riemann-Hilbert map

Vladimir Marković, Ognjen Tošić

Given a pair $(X, \nabla)$ , consisting of a closed Riemann surface $X$ and a holomorphic connection $\nabla$ on the trivial principal bundle $X \times SL_{2} (C) \to X$ ,…

math.DG2024

Constant energy families of harmonic maps

Ognjen Tošić

For a negatively curved manifold $M$ and a continuous map $ψ : Σ \to M$ from a closed surface $Σ$ , 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…