Caratheodory's conjecture on umbilical points of convex surfaces

Geometry Topology Seminar
Monday, January 24, 2011 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Mohammad Ghomi – Ga Tech
John Etnyre
Caratheodory's famous conjecture, dating back to 1920's, states that every closed convex surface has at least two umbilics, i.e., points where the principal curvatures are equal, or, equivalently, the surface has contact of order 2 with a sphere. In this talk I report on recent work with Ralph howard where we apply the divergence theorem to obtain integral equalities which establish some weak forms of the conjecture.