Attaching handles to Delaunay nodoids

Frank Pacard and Harold Rosenberg

Vol. 266 (2013), No. 1, 129–183

DOI: 10.2140/pjm.2013.266.129

Abstract

For all m ∈ ℕ −{0}, we prove the existence of a one-dimensional family of genus m, constant mean curvature (equal to 1) surfaces which are complete, immersed in ℝ³, and have two Delaunay ends asymptotic to nodoidal ends. Moreover, these surfaces are invariant under the group of isometries of ℝ³ leaving a horizontal regular polygon with m + 1 sides fixed.

Keywords

constant mean curvature surfaces, Delaunay surfaces

Mathematical Subject Classification 2010

Primary: 53C42

Secondary: 53A10

Milestones

Received: 31 July 2012

Revised: 16 December 2012

Accepted: 26 December 2012

Published: 23 September 2013