2016/05/31 by Song Dai, Dai, Song, Qiongling Li +1 · 2 citations
Mathematics · #53C21 #58D27 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1605.09596
openalex publication_date 2016/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a reductive representation ρ: π1(S)→ G, there exists a ρ-equivariant harmonic map f from the universal cover of a fixed Riemann surface Σ to the symmetric space G/K associated to G. If the Hopf differential of f vanishes, the harmonic map is then minimal. In this paper, we investigate the properties of immersed minimal surfaces inside symmetric space associated to a subloci of Hitchin component: qn and qn-1 case. First, we show that the pullback metric of the minimal surface dominates a constant multiple of the hyperbolic metric in the same conformal class and has a strong rigidity property. Secondly, we show that the immersed minimal surface is never tangential to any flat inside the symmetric space. As a direct corollary, the pullback metric of the minimal surface is always strictly negatively curved. In the end, we find a fully decoupled system to approximate the coupled Hitchin system.