Flux for Bryant surfaces and applications to embedded ends of finite total curvature

Details Flux for Bryant surfaces and applications to embedded ends of finite total curvature Flux for Bryant surfaces and applications to embedded ends of finite total curvature

2003-03-25

arxiv.org/abs/math/0303307v1

Illinois J. Math. 47 (3), 2003, 667-698

Mathematics

Differential Geometry

31 pages, 1 figure, submitted to Illinois Journal of Mathematics

Scientific paper

We compute the flux of Killing fields through ends of constant mean curvature 1 in hyperbolic space, and we prove a result conjectured by Rossman, Umehara and Yamada : the flux matrix they have defined is equivalent to the flux of Killing fields. We next give a geometric description of embedded ends of finite total curvature. In particular, we show that we can define an axis for these ends that are asymptotic to a catenoid cousin. We also compute the flux of Killing fields through these ends, and we deduce some geometric properties and some analogies with minimal surfaces in Euclidean space.

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