The classical theory of minimal and constant mean curvature surface theory with an emphasis on the uniqueness of examples found by Euler, Delaunay, Scherk  and Riemann.

Bill Meeks (U. Mass)

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 the constraint that the surfaces satisfy 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 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.

Colloquium, Department of Mathematics, Rice University
February 12, 2009 4-5PM, HB 227


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