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Fall 2003 Flux for Bryant surfaces and applications to embedded ends of finite total curvature
Benoît Daniel
Illinois J. Math. 47(3): 667-698 (Fall 2003). DOI: 10.1215/ijm/1258138187

Abstract

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 defined by these authors 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 if such an end is asymptotic to a catenoid cousin, then we can associate an axis to it. We also compute the flux of Killing fields through these ends, and we deduce some geometric properties and analogies to minimal surfaces in Euclidean space.

Citation

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Benoît Daniel. "Flux for Bryant surfaces and applications to embedded ends of finite total curvature." Illinois J. Math. 47 (3) 667 - 698, Fall 2003. https://doi.org/10.1215/ijm/1258138187

Information

Published: Fall 2003
First available in Project Euclid: 13 November 2009

zbMATH: 1043.53010
MathSciNet: MR2007230
Digital Object Identifier: 10.1215/ijm/1258138187

Subjects:
Primary: 53A10
Secondary: 53A35, 53C42

Rights: Copyright © 2003 University of Illinois at Urbana-Champaign

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Vol.47 • No. 3 • Fall 2003
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