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On the Branch Point Problem for Minimal SurfacesGeometry/Topology
|Speaker:||Tony Tromba, UC Santa Cruz|
|Start time:||Tue, Sep 27 2011, 4:10PM|
The beautiful question of whether area minimizing surfaces in Plateau's Problem are immersed or not had been open for some 40 years before it was resolved by Bob Osserman around 1970. Actually, his proof that Absolutely Area Minimizing Surfaces are immersed in the interior of domains was incomplete and was later completed by Osserman, Gulliver and Royden. Their often quoted proof is quite long and rather sophisticated and only a very few people in the world have read it in its entirety. We outline an entirely new approach based on Calculus and Elementary Complex Analysis which yields a much stronger result and makes it very clear why the theorem is true. We will present the entire history of the problem from its origins and finally will indicate how the new method can be applied to the heretofore open problem of whether or not minimal surfaces spannining smooth contours are immersed up to and including a smooth boundary.