Generic non-uniqueness of complete H-surfaces embedded in ℍ³

2016/02/05 by Cagri Haciyusufoglu, Haciyusufoglu, Cagri
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1602.02006

9 pages, 2 figures

arxiv created 2016/02/05 · arxiv updated 2016/02/08

Abstract

We prove that, given |H|<1, a generic simple closed curve embedded in the asymptotic boundary of ℍ³ (with respect to the supremum metric) bounds more than one complete surface embedded in ℍ³ which has constant mean curvature H. We remark that this is not true for the space of simple closed C¹-curves.

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