2020/07/20 by Инканг Ким, Xueyuan Wan, Kim, Inkang +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2007.10027
openalex publication_date 2020/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the paper, we consider the harmonic maps between surfaces Σ and S in the homotopy class of a (branched) covering map u0. We prove the uniqueness of critical points of energy function and the injectivity of Hopf differential if u0 is a covering map. On the other hand, if u0 is a branched covering, we show that the uniqueness of critical points fails if u0 is a non-simple branched covering, and prove the injectivity of Hopf differential Φ:\mcT(S)→ \opQD(Σ,g) when g=[u0^* h] for some hyperbolic metric h on S.