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Session 11. Geometric Analysis and Related Topics
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Ricci flow of regions with curvature bounded below in dimension three |
Miles Simon, University of Magdeburg, Germany
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We consider smooth complete solutions to Ricci flow with bounded
curvature on manifolds without boundary in
dimension three. Assuming a
ball at time zero of radius one has curvature bounded from below by \(-1\), then
we prove estimates which show that compactly contained subregions of
this ball will be smoothed out by the Ricci flow for a short but well
defined time interval.
The estimates we obtain depend on the initial volume of the ball and
the distance from the compact region to the boundary of the initial
ball. They do not depend on the upper bound of the curvature on the ball at time zero.
Versions of these estimates for balls of radius \(r\) follow using
scaling arguments.
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