2001/02/05 by Masatoshi Kokubu, Kokubu, Masatoshi, Masaaki Umehara +3 · 1 citation
Mathematics · #53A07 #53A10 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #Spectral Theory in Mathematical Physics #math.DG #msc:53A07 #msc:53A10 #msc:53C42
paper · pdf · doi:10.48550/arxiv.math/0102037
6 pages
arxiv created 2001/02/05 · openalex publication_date 2001/02/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the previous paper, Takahasi and the authors generalized the theory of minimal surfaces in Euclidean n-space to that of surfaces with holomorphic Gauss map in certain class of non-compact symmetric spaces. It also includes the theory of constant mean curvature one surfaces in hyperbolic 3-space. Moreover, a Chern-Osserman type inequality for such surfaces was shown. Though its equality condition is not solved yet, the authors have noticed that the equality condition of the original Chern-Osserman inequality itself is not found in any literature except for the case n=3, in spite of its importance. In this paper, a simple geometric condition for minimal surfaces that attains equality in the Chern-Osserman inequality is given. The authors hope it will be a useful reference for readers.