Perturbed cone theorems for proper harmonic maps

2023/12/19 by Renan Assimos, Assimos, Renan, Balázs Márk Békési +3
Mathematics · #53A10 #53C12 #53C42 #53C43 #58E20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2312.12375

openalex publication_date 2023/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inspired by the halfspace theorem for minimal surfaces in ℝ³ of Hoffman-Meeks, the halfspace theorem of Rodriguez-Rosenberg, and the cone theorem of Omori, we derive new non-existence results for proper harmonic maps into perturbed cones in ℝⁿ, horospheres in ℍⁿ and also into perturbed Riemannian cones. The technical tool in use is an extension of the foliated maximum principle appearing in Assimos-Jost to the non-compact setting.

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