## Regularity and Geometry of Real Algebraic Convex Hypersurfaces

Series
Geometry Topology Working Seminar
Time
Friday, January 29, 2010 - 2:00pm for 1.5 hours (actually 80 minutes)
Location
Skiles 269
Speaker
Mohammad Ghomi – School of Mathematics, Georgia Tech
Organizer
Meredith Casey
We prove that convex hypersurfaces M in R^n which are level sets of functions f: R^n --> R are C^1-regular if f has a nonzero partial derivative of some order at each point of M. Furthermore, applying this result, we show that if f is algebraic and M is homeomorphic to R^(n-1), then M is an entire graph, i.e., there exists a line L in R^n such that M intersects every line parallel L at precisely one point. Finally we will give a number of examples to show that these results are sharp.