Mean Curvature Flow of Tori of Revolution

Lewis & Clark College
Talk Abstract
Mean curvature flow is the $L^2$ gradient flow of the volume functional on embedded surfaces. As a nonlinear system of parabolic equations, its behavior is quite complicated, but generally solutions become more spherical over time as their volume decreases. The evolution of tori under this flow is of interest because their non-trivial topology prevents them from becoming round. This leads to the formation of a variety of singularities. In this talk, I will focus on tori of revolution, which reduces the problem to a version of planar curve shortening flow. From this viewpoint, the possible singularities can be classified and, in some cases, their asymptotic behavior can be determined.
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Time Slot