Tangent cones and regularity of real hypersurfaces

Analysis Seminar
Wednesday, April 14, 2010 - 14:00
1 hour (actually 50 minutes)
Skiles 269
Georgia Tech
The tangent cone of a set X in R^n at a point p of X is the limit of all rays which emanate from p and pass through sequences of points p_i of X as p_i converges to p. In this talk we discuss how C^1 regular hypersurfaces of R^n may be characterized in terms of their tangent cones. Further using the real nullstellensatz we prove that convex real analytic hypersurfaces are C^1, and will also discuss some applications to real algebraic geometry.