Ancient solutions of extrinsic curvature flows with curvature pinching
speaker: Carlo Sinestrari (Università di Roma "Tor Vergata")abstract: We consider compact convex hypersurfaces evolving by mean curvature flow which are ancient, that is, defined for all negative times. Solutions with these properties occur as the limit of rescalings near a singularity of a general mean convex solution of the flow. The easiest example is a shrinking sphere, but there are other knwon examples having an oval shape which becomes more and more eccentric for negative times.
In this talk we consider various sufficient conditions which ensure that our solution is a shrinking sphere. Examples are: a uniform pinching on the principal curvatures, a growth rate assumption on the diameter, a bound on the ratio of outer and inner radius, a bound on the isoperimetric ratio. These results are in collaboration with G. Huisken.
The characterization of the shrinking sphere via the uniform pinching property has been also obtained in more general contexts, such as higher codimensional mean curvature flow, or other extrinsic curvature flows (in collaboration with S. Risa).
timetable:
Tue 21 Feb, 15:00 - 16:00, Aula Dini
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