Bifurcating nodoids

Details Bifurcating nodoids Bifurcating nodoids

2002-07-24

arxiv.org/abs/math/0207224v1

Mathematics

Differential Geometry

18 pages. To appear in SISTAG Commemorative Volume in the AMS Contemporary Math Series

Scientific paper

All complete, axially symmetric surfaces of constant mean curvature in R^3 lie in the one-parameter family D_tau of Delaunay surfaces. The elements of this family which are embedded are called unduloids; all other elements, which correspond to parameter value tau element in R^-, are immersed and are called nodoids. The unduloids are stable in the sense that the only global constant mean curvature deformations of them are to other elements of this Delaunay family. We prove here that this same property is true for nodoids only when tau is sufficiently close to zero (this corresponds to these surfaces having small `necksizes'). On the other hand, we show that as tau decreases to negative infinity, infinitely many new families of complete, cylindrically bounded constant mean curvature surfaces bifurcate from this Delaunay family. The surfaces in these branches have only a discrete symmetry group.

Affiliated with

Also associated with

No associations

Rating

Bifurcating nodoids does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bifurcating nodoids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bifurcating nodoids will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-226864