Paper · Jan 8, 2017
Parabolic Omori-Yau maximum principle for mean curvature flow and some applications
As on arXiv
Abstract
We derive a parabolic version of Omori-Yau maximum principle for a proper mean curvature flow when the ambient space has lower bound on -sectional curvature. We apply this to show that the image of Gauss map is preserved under a proper mean curvature flow in euclidean spaces with uniform bounded second fundamental forms. This generalizes the result of Wang for compact immersions. We also prove a Omori-Yau maximum principle for properly immersed self-shrinkers, which improves a result in.
- Submitted
- Jan 8, 2017
- Last revised
- Jan 21, 2017 (v2)
- Subjects
- math.DG
- Journal
- J. Geom. Anal. 28, No. 4, 3183-3195 (2018)
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Background reading
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In the guidebook
- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.