Moduli of Flat Conformal Structures of Hyperbolic Type

2008/04/04 by Graham Smith, Smith, Graham · 2 citations
Mathematics · #35J60 #53A30 (Primary) #53C21 #53C42 #58J05 (Secondary) #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #math.DG #msc:35J60 #msc:53A30 #msc:53C21 #msc:53C42 #msc:58J05

paper · pdf · doi:10.48550/arxiv.0804.0744

TeX referencing errors corrected

openalex publication_date 2008/04/04 · arxiv created 2009/08/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

To each flat conformal structure (FCS) of hyperbolic type in the sense of Kulkarni-Pinkall, we associate, for all θ∈[(n-1)π/2,nπ/2[ and for all r>\opTan(θ/n) a unique immersed hypersurface Σ_r,θ=(M,i_r,θ) in ℍⁿ⁺¹ of constant θ-special Lagrangian curvature equal to r. We show that these hypersurfaces smoothly approximate the boundary of the canonical hyperbolic end associated to the FCS by Kulkarni and Pinkall and thus obtain results concerning the continuous dependance of the hyperbolic end and of the Kulkarni-Pinkall metric on the flat conformal structure.

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