2025/11/14 by J. Maxwell Riestenberg, Riestenberg, J. Maxwell, Peter Smillie +1
Mathematics · #53C35 #53C43 #58E20 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2511.11469
openalex publication_date 2025/11/14 · openalex created_date 2025/11/18 · openalex updated_date 2026/08/01
We give a sufficient criterion, which we call stability, for a coarse Lipschitz map f from a complete manifold X with Ricci curvature bounded below to a proper Hadamard space Y to be within bounded distance of a harmonic map. We prove uniqueness of the harmonic map under additional assumptions on X and Y. Using this criterion, we prove a significant generalization of the Schoen-Li-Wang conjecture on quasi-isometric embeddings between rank 1 symmetric spaces. In particular, under a natural generalization of the quasi-isometric condition, we remove the assumption that the target has rank 1. This allows us to define a universal Hitchin component for each PGLd(ℝ), generalizing universal Teichmüller space, and show that it can be described both as a space of quasi-symmetric positive maps from \mathbbRP1 to the flag variety, and as a space of harmonic maps.