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Geometric Analysis Seminar

Existence of Mean Curvature Flow Singularities with Bounded Mean Curvature

Maxwell Stolarski (Arizon State University)

Location:  via Zoom,
Date & time: Tuesday, 22 September 2020 at 2:50PM - 3:50PM

Abstract: Hypersurfaces moving by mean curvature flow often become singular in finite time. At this time, the flow may no longer be continued smoothly. The extension problem asks, "If M(t) is a solution to mean curvature flow defined up to time T, what conditions ensure that we may smoothly extend this solution to slightly later times?" For example, a result of Huisken says that if the 2nd fundamental forms of the evolving hypersurfaces remain uniformly bounded, then the mean curvature flow can be extended. One might then ask if a uniform bound on the mean curvature suffices to extend the flow. We'll discuss recent work that shows the answer is "no" in general, that is, there exist mean curvature flow solutions that become singular in finite time but have uniformly bounded mean curvature.

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