We prove rigidity theorems for ancient solutions of geometric flows of immersed submanifolds. Specifically, we find pinching conditions on the second fundamental form that characterize the shrinking sphere among compact ancient solutions for the mean curvature flow in codimension greater than one, and for some nonlinear curvature flows of hypersurfaces.
Risa, S., Sinestrari, C. (2019). Ancient Solutions of Geometric Flows with Curvature Pinching. THE JOURNAL OF GEOMETRIC ANALYSIS, 29, 1206-1232 [10.1007/s12220-018-0036-0].
Ancient Solutions of Geometric Flows with Curvature Pinching
Risa, Susanna;Sinestrari, Carlo
2019-01-01
Abstract
We prove rigidity theorems for ancient solutions of geometric flows of immersed submanifolds. Specifically, we find pinching conditions on the second fundamental form that characterize the shrinking sphere among compact ancient solutions for the mean curvature flow in codimension greater than one, and for some nonlinear curvature flows of hypersurfaces.File in questo prodotto:
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