### Regularity and Geometry of Real Algebraic Convex Hypersurfaces

- Series
- Geometry Topology Working Seminar
- Time
- Friday, January 29, 2010 - 14:00 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 269
- Speaker
- Mohammad Ghomi – School of Mathematics, Georgia Tech

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.