The Journal of Geometric Analysis

, Volume 29, Issue 2, pp 1206–1232 | Cite as

Ancient Solutions of Geometric Flows with Curvature Pinching

  • Susanna Risa
  • Carlo SinestrariEmail author


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.


Ancient solutions Mean curvature flow Gauss curvature flow Geometric flows 

Mathematics Subject Classification

53C44 35K55 



Carlo Sinestrari was partially supported by the research group GNAMPA of INdAM (Istituto Nazionale di Alta Matematica).


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Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly
  2. 2.Dipartimento di Ingegneria Civile e Ingegneria InformaticaUniversità di Roma “Tor Vergata”RomaItaly

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