Harmonic maps from the product of the hyperbolic planes to the hyperbolic space

2025/08/29 by Kazuo Akutagawa, Akutagawa, Kazuo, Y. Matsumoto +1
Mathematics · #53C43 (Primary) 58E20 #58J32 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2508.21384

openalex publication_date 2025/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An existence result is shown for the asymptotic Dirichlet problem for harmonic maps from the product of the hyperbolic planes to the hyperbolic space, where the Dirichlet data is given on the distinguished boundary (the product of the circles at infinity).

Citations

• Proper harmonic maps between asymptotically hyperbolic manifolds

Related

• Proper harmonic maps between asymptotically hyperbolic manifolds
• Approximate solutions to the Dirichlet problem for harmonic maps between hyperbolic spaces
• Harmonic extensions of quasisymmetric maps
• Asymptotic Dirichlet problem for harmonic maps and conformal geodesics
• New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation