Mathematics – Differential Geometry
Scientific paper
2011-07-22
Mathematics
Differential Geometry
Statement of main theorem extended to integral Brakke flows. Several typos corrected
Scientific paper
We show, for mean curvature flows in Euclidean space, that if one of the tangent flows at a given space-time point consists of a closed, multiplicity-one, smoothly embedded self-similar shrinker, then it is the unique tangent flow at that point. That is the limit of the parabolic rescalings does not depend on the chosen sequence of rescalings. Furthermore, given such a closed, multiplicity-one, smoothly embedded self-similarly shrinker $\Sigma$, we show that any solution of the rescaled flow, which is sufficiently close to $\Sigma$, with Gaussian density ratios greater or equal to that of $\Sigma$, stays for all time close to $\Sigma$ and converges to a possibly different self-similarly shrinking solution $\Sigma'$. The central point in the argument is a direct application of the Simon-{\L}ojasiewicz inequality to Huisken's monotone Gaussian integral for Mean Curvature Flow.
No associations
LandOfFree
Uniqueness of compact tangent flows in Mean Curvature Flow does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Uniqueness of compact tangent flows in Mean Curvature Flow, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uniqueness of compact tangent flows in Mean Curvature Flow will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-667304