Math Union

Details

Plateau's Problem, Minimal Surfaces and Geometric Inequalities

by Kry Lui | University of Toronto
Time: 14:00 — 15:30  (Monday, May. 09, 2011)
Location: BA6180, Bahen Center, 40 St George St
Abstract:
In 1930, Douglas and Rado solved the Plateau's problem: Given a simple closed Jordan curve, does there exist a soap film (2-D surface) that fills in the curve? Later on Courant (1936) found a simplified approach by modifying their methods. This presentation will start from discussing why the problem is hard and based on Courant's method, tries to suggest a way to get started on solving this problem. The second part outlines the key ingredients in the proof. Time permitting, the last part mentions its connections to the isoperimetric inequality, perhaps also the systolic inequality, the scalar curvature and three-manifold theory.

Dates in this series

· Friday, Oct. 22, 2010: Mathematical Finance (Sebastian Jaimungal, Alan White, Yuri Lawryshyn, Chad McAlpine)
· Friday, Nov. 26, 2010: Panel Discussion on Mathematical Physics (Marco Gualtieri, Israel Michael Sigal, Jen Dodd, John Sipe)
· Friday, Mar. 11, 2011: Medicine and its Models: A discussion (Sivabal Sivaloganathan, Michael Milosevic, Sheila Singh)
· Tuesday, Mar. 29, 2011: Numbers and Nature (James Robert Brown)
· Monday, May. 09, 2011: Plateau's Problem, Minimal Surfaces and Geometric Inequalities (Kry Lui)
· Thursday, Jul. 14, 2011: A Painless Introduction to Holomorphic Dynamics and the Mandelbrot Set (John Yang)
· Thursday, Jul. 21, 2011: TBA (Edith Viau)
· Friday, Aug. 12, 2011: An Introduction to p-adic Analysis (Joshua Seaton)