Mean curvature 1 surfaces in hyperbolic 3-space with low total curvature II

Mathematics – Differential Geometry

Scientific paper

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19 pages, 5 figures

Scientific paper

In this work, complete constant mean curvature 1 (CMC-1) surfaces in
hyperbolic 3-space with total absolute curvature at most 4 pi are classified.
This classification suggests that the Cohn-Vossen inequality can be sharpened
for surfaces with odd numbers of ends, and a proof of this is given.

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