New constructions of volume-critical submanifolds of the sphere

  • Date: 12/05/2006

Adrian Butscher (University of Toronto, Scarborough)


University of British Columbia


Constant mean curvature hypersurfaces in S^n are critical points of the
(n-1)-volume functional subject to an enclosed-volume constraint
whereas contact-stationary Legendrian (CSL) submanifolds of S^{2n+1}
are n-dimensional submanifolds tangent to the contact distribution
whose n-volume is critical amongst all Legendrian competitors. I will
present new constructions of CMC and CSL submanifolds in spheres using
gluing techniques and a good understanding of the isometries of the
ambient sphere. I will also highlight some similarities between the
world of CSL submanifolds and the world of CMC hypersurfaces.

Other Information: 

DG-MP-PDE Seminar 2006