University of Toronto
                  PDE/Applied Math/Analysis Seminar
                           Friday February 9



SPEAKER:  Adrian Butscher (Toronto)

TITLE:    New constructions of submanifolds of the sphere which 
          are critical  points of the volume functional.

ABSTRACT: If one searches for k-dimensional submanifolds with 
          critical k-dimensional volume in a Riemannian manifold, 
          then one is led  towards elliptic partial differential 
          equations involving the mean  curvature vector of the 
          submanifold.  I will present new  constructions of 
          volume-critical submanifolds of the sphere in two  
          contexts: hypersurfaces with constant mean curvature 
          in spheres of any dimension; and Legendrian submanifolds 
          in spheres of odd  dimension that are stationary under 
          variations preserving the contact structure.  These are 
          constructed by solving the associated  elliptic PDE using 
          singular perturbation theory.  I will then highlight some 
          of the analytic and geometric similarities between  
          these two contexts.



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

2006-2007 organizers:
          Pieter Blue           pblue@ math.toronto.edu
          Almut Burchard        almut@ math.toronto.edu
          Robert McCann		mccann@ math.toronto.edu
------------------------------------------------------------------