2020/05/28 by Song Dai, Qiongling Li
Mathematics · #Fibration #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Holonomy #Homotopy #Mathematics #Moduli space #Pure mathematics #math.DG #math.GT
paper · pdf · doi:10.1112/plms.12431
41 pages, comments are welcome
arxiv created 2020/05/28 · openalex publication_date 2022/03/02 · openalex created_date 2022/03/05 · arxiv updated 2022/03/14 · openalex updated_date 2026/08/06
In this article, we show some domination results on the Hitchin fibration, mainly focusing on the n-Fuchsian fibers. More precisely, we show the energy density of associated harmonic map of an n-Fuchsian representation dominates the ones of all other representations in the same Hitchin fiber, which implies the domination of topological invariants: translation length spectrum and entropy. As applications of the energy density domination results, we obtain the existence and uniqueness of equivariant minimal (or maximal) surfaces in certain product Riemannian (or pseudo-Riemannian) manifold. Our proof is based on establishing an algebraic inequality generalizing a GIT theorem of Ness on the nilpotent orbits to general orbits.