CMC Surfaces

Bubbletons

Constant mean curvature cylinders in euclidean 3-space

Delaunay bubbletons are constructed by dressing a Delaunay surface with a product of simple factor dressingsĀ [3,1,2].

A two-lobed bubble on a straight cylinder.
Two-lobed bubbles on a Delaunay unduloid and nodoid.
Double bubbleton: two-lobed and three-lobed bubbles on a Delaunay unduloid.
Two-lobed bubbles on a Delaunay unduloid and nodoid.
Two-lobed bubbleton on a Delaunay twizzler.
A two-lobed bubble colides with a 3-lobed bubble.

References

  1. M. Melko and I. Sterling, Application of soliton theory to the construction of pseudospherical surfaces in R3, Ann. Global Anal. Geom. 11 (1993), no. 1, 65—107 [1201412].
  2. M. Melko and I. Sterling, Integrable systems, harmonic maps and the classical theory of surfaces, Harmonic maps and integrable systems, Aspects Math., E23, Friedr. Vieweg, Braunschweig (1994), 129—144 [1264184].
  3. I. Sterling and H. Wente, Existence and classification of constant mean curvature multibubbletons of finite and infinite type, Indiana Univ. Math. J. 42 (1993), no. 4, 1239—1266 [1266092].