PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Sergei Tabachnikov.

Title:The four vertex property and topology of surfaces with constant curvature
Seminar:MASS Colloquium
Speaker:M. Ghomi, Georgia Tech
Abstract:
The classical four vertex theorem of Kneser states that any simple closed curve in the plane has four vertices, i.e., points where the curvature has a local max or min. This result has had many generalizations over the years. In particular, Pinkall has shown that any closed curve in the plane or the sphere which bounds a a compact immersed surface has four vertices. This result holds in the hyperbolic plane as well. In this talk we give an elementary introduction to these results, and present some further generalizations due to the speaker. In particular we show that the sphere is the only compact surface of constant curvature in which every closed curve which bounds an immersed surface has four vertices. Also, we give a similar characterization for the disk among all compact surfaces with boundary.

Room Reservation Information

Room Number:MB113
Date:09 / 11 / 2008
Time:02:30pm - 03:20pm