Cylindrical estimates for mean curvature flow of hypersurfaces in CROSSes |
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Authors: | Giuseppe Pipoli Carlo Sinestrari |
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Affiliation: | 1.Institut Fourier, Laboratoire de mathématiques,Université Grenoble Alpes,Gières,France;2.Dipartimento di Ingegneria Civile e Ingegneria Informatica,Università di Roma “Tor Vergata”,Rome,Italy |
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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. |
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