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DESCRIPTION:Speaker: Felix Schulze (University of Warwick)\n\nTitle: \n\nMe
an curvature flow with generic initial data\n\nAbstract: Mean curvature flo
w is the gradient flow of the area functional and constitutes a natural geo
metric heat equation on the space of hypersurfaces in an ambient Riemannian
manifold. It is believed\, similar to Ricci Flow in the intrinsic setting\
, to have the potential to serve as a tool to approach several fundamental
conjectures in geometry. The obstacle for these applications is that the fl
ow develops singularities\, which one in general might not be able to class
ify completely. Nevertheless\, a well-known conjecture of Huisken states th
at a generic mean curvature flow should have only spherical and cylindrical
singularities. As a first step in this direction Colding-Minicozzi have sh
own in fundamental work that spheres and cylinders are the only linearly st
able singularity models. As a second step toward Huisken's conjecture we sh
ow that mean curvature flow of generic initial closed surfaces in R^3 avoid
s asymptotically conical and non-spherical compact singularities. The main
technical ingredient is a long-time existence and uniqueness result for anc
ient mean curvature flows that lie on one side of asymptotically conical or
compact self-similarly shrinking solutions. This is joint work with Otis C
hodosh\, Kyeongsu Choi and Christos Mantoulidis.
DTEND:20211102T200500Z
DTSTAMP:20220119T053447Z
DTSTART:20211102T185000Z
LOCATION:
SEQUENCE:0
SUMMARY:Geometric Analysis Seminar
UID:tag:localist.com\,2008:EventInstance_37563433011459
URL:https://calendar.utk.edu/event/geometric_analysis_seminar_5777
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