Gauss Curvature Flow on Surfaces of Revolution
Time and place
1 PM on Thursday, April 15th, 2010; NAC 6113
Thalia Jeffres (Wichita State University)
Abstract
The fundamental quantity that describes the shape of a smooth surface is its "curvature,'' which is exactly that - a measure of how sharply the surface curves. It can be defined in turn using the Calc III notion of the curvature of a curve... or described entirely in pictures, for those who have not had Calc III. A surface is said to evolve under curvature flow if it continuously changes its shape in time in the following way: Each point moves in the direction perpendicular to the surface, and at a rate proportional to the curvature at that point. Thus, points located on portions of the surface that bend more sharply move faster than points where the surface is flatter. I will describe such a problem on surfaces of revolution. At every opportunity, I will draw connections to material in calculus courses, and I will define all relevant objects and quantities in two ways, by giving their precise definitions, and by drawing pictures and giving intuitive ideas. In this way, the talk will be accessible to all.
