Cylindrical estimates for mean curvature flow of hypersurfaces in CROSSes

We consider the mean curvature flow of a closed hypersurface in the complex or quaternionic projective space. Under a suitable pinching assumption on the initial data, we prove apriori estimates on the principal curvatures which imply that the asymptotic profile near a singularity is either strictly...

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Bibliographic Details
Published in:Annals of global analysis and geometry 2017-03, Vol.51 (2), p.179-188
Main Authors: Pipoli, Giuseppe, Sinestrari, Carlo
Format: Article
Language:English
Subjects:
Analysis
Curvature
Differential Geometry
Estimates
Euclidean geometry
Euclidean space
Geometry
Global Analysis and Analysis on Manifolds
Mathematical analysis
Mathematical Physics
Mathematics
Mathematics and Statistics
Singularities
Studies
Symmetry
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Summary:We consider the mean curvature flow of a closed hypersurface in the complex or quaternionic projective space. Under a suitable pinching assumption on the initial data, we prove apriori estimates on the principal curvatures which imply that the asymptotic profile near a singularity is either strictly convex or cylindrical. This result generalizes to a large class of symmetric ambient spaces the estimates obtained in the previous works on the mean curvature flow of hypersurfaces in Euclidean space and in the sphere.
ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-016-9530-4