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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Received 27 March 1997; in final form 11 June 1998
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López, R. Constant Mean Curvature Surfaces with Boundaryin Hyperbolic Space. Mh Math 127, 155–169 (1999). https://doi.org/10.1007/s006050050030
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DOI: https://doi.org/10.1007/s006050050030