Strong spherical rigidity of ancient solutions of expansive curvature flows

DOI10.1112/blms.12308zbMath1442.53069arXiv1907.12319OpenAlexW3100604322MaRDI QIDQ5110602

Susanna Risa, Carlo Sinestrari

Publication date: 21 May 2020

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.12319

zbMATH Keywords

extrinsic curvaturehomothethic sphererigidity of solutions

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Flows related to mean curvature (53E10)

Related Items (5)

Collapsing and noncollapsing in convex ancient mean curvature flow ⋮ Aleksandrov reflection for extrinsic geometric flows of Euclidean hypersurfaces ⋮ Non-homothetic convex ancient solutions for flows by high powers of curvature ⋮ Nonhomogeneous expanding flows in hyperbolic spaces ⋮ Ancient mean curvature flows out of polytopes

Cites Work

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• Classification of convex ancient solutions to curve shortening flow on the sphere
• Ancient solutions of the mean curvature flow
• Solitons for the inverse mean curvature flow
• On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures
• Convex solutions to the mean curvature flow
• Convex ancient solutions of the mean curvature flow
• Flow of nonconvex hypersurfaces into spheres
• Higher regularity of the inverse mean curvature flow
• Geometric aspects of Aleksandrov reflection and gradient estimates for parabolic equations
• The inverse mean curvature flow and the Riemannian Penrose inequality
• Classification of prime 3-manifolds with \(\sigma\) invariant greater than \(\mathbb RP^3\)
• Aleksandrov reflection and nonlinear evolution equations. I: The \(n\)-sphere and \(n\)-ball
• Formal asymptotic expansions for symmetric ancient ovals in mean curvature flow
• Ancient solutions of geometric flows with curvature pinching
• Non-scale-invariant inverse curvature flows in Euclidean space
• The nature of singularities in mean curvature flow of mean-convex sets
• Uniqueness theorems for surfaces in the large. I, II, III, IV, V
• Aleksandrov reflection and geometric evolution of hypersurfaces

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