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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Asymptotics of ends of constant mean curvature surfaces with bubbletons


Author: Shimpei Kobayashi
Journal: Proc. Amer. Math. Soc. 136 (2008), 1433-1443
MSC (2000): Primary 53A10
Published electronically: December 10, 2007
MathSciNet review: 2367117
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Abstract: A constant mean curvature surface with bubbletons is defined by the loop group action on the set of extended framings for constant mean curvature surfaces by simple factors. Classically such surfaces were obtained by the transformation of tangential line congruences, the so-called Bianchi-Bäcklund transformations.

In this paper, we consider constant mean curvature surfaces with Delaunay ends in three-dimensional space forms $ \mathbb{R}^3$, $ S^3$ and $ H^3$ and their surfaces with bubbletons for which the topology is preserved. We show that the ends of such surfaces are again asymptotic to Delaunay surfaces.


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Additional Information

Shimpei Kobayashi
Affiliation: School of Information Environment, Tokyo Denki University, Chiba 270-1382, Japan
Email: shimpei@sie.dendai.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09137-X
PII: S 0002-9939(07)09137-X
Received by editor(s): April 11, 2006
Received by editor(s) in revised form: February 15, 2007
Published electronically: December 10, 2007
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.