Constant Mean Curvature Surfaces with Boundaryin Hyperbolic Space |
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Authors: | Rafael López |
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Institution: | (1) Department of Natural Sciences, Faculty of Engineering, Tokyo Denki University, Chiba, 270-1355, Japan |
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Abstract: | We study constant mean curvature compact surfaces immersed in hyperbolic space with non-empty boundary (=H-surfaces). We prove that the only H-surfaces with boundary circular and 0≤∣H∣≤1, are the umbilical examples. When the surface is embedded, conditions to be umbilical are given. Finally, we characterize umbilical surfaces bounded by a circle among all H-discs with small area. |
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