Abstract:Part of the classical theory of minimal surfaces in
three-dimensional Euclidean space deals with the asymptotic properties of
complete embedded classical examples M. This theory then lends itself to
obtain classification results of the surfaces subject to some geometric or topological constraint.
For example, if M is simply-connected, then recent work of Colding-Minicozzi and of
Meeks-Rosenberg demonstrates that the only examples are the plane and the
helicoid. Very recently, Meeks and Tinaglia have extended this result to
show that a complete, simply-connected, embedded surface of non-zero constant mean
curvature M must be a sphere, thereby completing a more general
classification question. My talk will be for a general audience and
undergraduates should enjoy the computer graphics images and the history
presented. |