University of Toronto
                  PDE/Applied Math/Analysis Seminar
                    Friday February 10, 12:10-1pm
                          2185 Bahen Center      


               PLEASE NOTE  SPECIAL TIME AND LOCATION;
                   LUNCH WITH THE SPEAKER TO FOLLOW.



SPEAKER:  Benjamin Stephens (MIT)

TITLE:    Thread-wire surfaces.

ABSTRACT: I began my thesis by doing experiments with soap-
          water, wire and thread. I will show videos of these 
          experiments and talk about resulting conjectures and 
          theorems regarding the "thread problem." This 
          problem asks for least-area surfaces between a fixed 
          boundary and a flexible boundary with constrained 
          length. I will show how near-wire solutions to the 
          thread problem consist of Lipschitz graphs lying 
          near maxima of wire curvature.

          Solutions to the thread-problem typically exhibit 
          cusp-like corners. There are interesting questions 
          about how the surface normal behaves as one 
          approaches such a corner.  I will show what I can 
          prove and talk about how further results at the 
          corner could imply a finiteness result for generic 
          wires.  Understanding corner behavior is also 
          necessary for showing a thread-surface analog to 
          Carmo-Barbosa's beautiful stability result for wires 
          with total curvature less than 4 Pi.

          If you're interested, see www.bkstephens.net for 
          related videos.


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University of Toronto PDE/Applied Math/Analysis Seminar 
http://www.math.toronto.edu/appmath/

2005-2006 organizers:
          Pieter Blue           pblue@ math.toronto.edu
          Almut Burchard        almut@ math.toronto.edu
          Bob Jerrard           rjerrard@ math.toronto.edu
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