Gergen Lecture #4
Tuesday, November 22, 2016, 1:30pm, Physics Room 235
Simon Brendle (Columbia University)
Singularity formation in fully nonlinear curvature flows

Abstract:

We discuss joint work with Gerhard Huisken on a fully nonlinear flow for two-convex hypersurfaces. Unlike mean curvature flow, this flow preserves two-convexity in any ambient Riemannian manifold. Moreover, the flow becomes extinct in finite time if the ambient manifold has nonnegative sectional curvature. For this flow, we establish various a-priori estimates, such as a convexity estimate, a cylindrical estimate, and a pointwise derivative estimate for the curvature. Using these estimates, we are able to extend the flow beyond singularities using a surgery construction in the spirit of Hamilton and Perelman. This is the first construction of this type in the fully nonlinear setting.

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