Asymptotics of ends of constant mean curvature surfaces with bubbletons

Kobayashi, Shimpei

doi:10.1090/S0002-9939-07-09137-X

Asymptotics of ends of constant mean curvature surfaces with bubbletons
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Proc. Amer. Math. Soc. 136 (2008), 1433-1443 Request permission

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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