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Minimal Surface Seminar

Tuesday, October 25, 2016 - 4:30pm

Rob Kusner

UMass

Location

University of Pennsylvania

DRL 4N30

Fine to attend this talk, even if you missed part 1 past week.

Minimal surfaces are the mathematical model for soap films: tension forces in balance (mean curvature zero) at every point, or (equivalently) critical for the area functional, or (equivalently) conformally parametrized by harmonic functions.  We'll begin with some classical examples, explain the first & second variation formulas for area and their consequences, and sketch some constructions of minimal surfaces: via solution to Plateau's problem (and Schwarz reflection), via the Weierstrass representation, etc.  Then we'll discuss some relatively recent results about complete, properly embedded minimal surfaces, such as topological uniqueness (Frohman-Meeks) and topological obstructions (Collin-K.....-Meeks-Rosenberg), asymptotic behavior (Osserman, Schoen, Jorge-Meeks, Colding-Minicozzi, Meeks-Rosenberg...) and moduli space theory.