Mathematics – Differential Geometry
Scientific paper
2001-02-05
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.
Kokubu Masatoshi
Umehara Masaaki
Yamada Kotaro
No associations
LandOfFree
Minimal surfaces that attain equality in the Chern-Osserman inequality does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Minimal surfaces that attain equality in the Chern-Osserman inequality, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Minimal surfaces that attain equality in the Chern-Osserman inequality will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-104845