The behaviour of the mean curvature flow for pinched submanifolds in rank one symmetric spaces

zbMath1506.53097MaRDI QIDQ2080655

Naoyuki Koike

Publication date: 10 October 2022

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/osaka-journal-of-mathematics/volume-59/issue-4/The-behaviour-of-the-mean-curvature-flow-for-pinched-submanifolds/5543ojm.full

zbMATH Keywords

totally geodesic submanifoldcollapse to a pointpinching conditiontraceless second fundamental formpreservability

Mathematics Subject Classification ID

Differential geometry of symmetric spaces (53C35) Flows related to mean curvature (53E10)

Cites Work

• Unnamed Item
• Mean curvature flow of higher codimension in hyperbolic spaces
• Deforming hypersurfaces of the sphere by their mean curvature
• Mean curvature flow of pinched submanifolds to spheres
• Flow by mean curvature of convex surfaces into spheres
• Asymptotic behavior for singularities of the mean curvature flow
• Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature
• An intrinsic rigidity theorem for minimal submanifolds in a sphere
• Shortening embedded curves
• Mean curvature flow of pinched submanifolds of \(\mathbb{CP}^n\)
• Real hypersurfaces in quaternionic projective space
• Three-manifolds with positive Ricci curvature
• Riemannian manifolds with positive mean curvature
• Sobolev and isoperimetric inequalities for riemannian submanifolds
• PINCHING THEOREMS FOR A COMPACT MINIMAL SUBMANIFOLD IN A COMPLEX PROJECTIVE SPACE

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