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

Pipoli, G., Sinestrari, C. (2017). Cylindrical estimates for mean curvature flow of hypersurfaces in CROSSes. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 51(2), 179-188 [10.1007/s10455-016-9530-4].

Cylindrical estimates for mean curvature flow of hypersurfaces in CROSSes

SINESTRARI, CARLO
2017-03-01

Abstract

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
mar-2017
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
Settore MAT/03 - GEOMETRIA
English
Con Impact Factor ISI
Mean curvature flow, Singularity formation, Complex and quaternionic projective spaces
Pipoli, G., Sinestrari, C. (2017). Cylindrical estimates for mean curvature flow of hypersurfaces in CROSSes. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 51(2), 179-188 [10.1007/s10455-016-9530-4].
Pipoli, G; Sinestrari, C
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/165798
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