Minimal surfaces that attain equality in the Chern-Osserman inequality

Details Minimal surfaces that attain equality in the Chern-Osserman inequality Minimal surfaces that attain equality in the Chern-Osserman inequality

2001-02-05

arxiv.org/abs/math/0102037v1

Mathematics

Differential Geometry

6 pages

Scientific paper

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.

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