Lagrangian mean curvature flow of pinched submanifolds of CPⁿ

2013/10/10 by Pipoli, Giuseppe, Sinestrari, Carlo
#53C44 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1310.2837

Abstract

We consider the evolution by mean curvature flow of Lagrangian submanifolds of the complex projective space CPⁿ. We prove that, if the initial value satisfies a suitable pinching condition, then the flow exists for all times and the manifold converges to a totally geodesic submanifold. As a corollary, we obtain that a Lagrangian submanifold satisfying our pinching condition is diffeomorphic to a real projective space.

Related

• Mean curvature flow of pinched submanifolds of \mathbbCPⁿ
• Mean Curvature Flow of High Codimension in Complex Projective Space
• Mean Curvature Flows of Lagrangian Submanifolds with Convex Potentials
• Mean curvature flow for pinched submanifolds in rank one symmetric spaces
• Mean curvature flow of arbitrary codimension in complex projective spaces