ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 53, 51 Sullivan, John M, University of Illinois, Urbana, USA Triunduloids: Embedded Constant-Mean-Curvature Surfaces with Three Ends We consider the moduli space of all almost embedded constant-mean-curvature surfaces with three ends and genus zero. These are called triunduloids because each end is asymptotically an unduloid (a Delaunay surface). Considering force balancing conditions and the conjugate-cousin minimal surface in S^{3} allows us to explicitly describe the moduli space of triunduloids, which is isomorphic to to space of triangles in S^{2}. Going around loops in this space creates new bubbles on the ends of the surface.