Inverse mean curvature flow of rotationally symmetric hypersurfaces

DOI10.1007/s00526-023-02469-8OpenAlexW3049202183MaRDI QIDQ2695762

Brian Harvie

Publication date: 5 April 2023

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.07490

zbMATH Keywords

inverse mean curvature flowhomothetically convergencemean-convex spherenon-star-shaped

Mathematics Subject Classification ID

PDEs on manifolds (35R01) Flows related to mean curvature (53E10)

Cites Work

• Lecture notes on mean curvature flow
• On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures
• Flow by mean curvature of convex surfaces into spheres
• The 6\(\pi\) theorem about minimal surfaces
• Asymptotic behavior for singularities of the mean curvature flow
• Interior estimates for hypersurfaces moving by mean curvature
• Flow of nonconvex hypersurfaces into spheres
• Higher regularity of the inverse mean curvature flow
• The quermassintegral inequalities for \(k\)-convex starshaped domains
• The heat equation shrinking convex plane curves
• A short note on the evolution of a surface by its mean curvature
• The existence of embedded minimal surfaces and the problem of uniqueness
• Volume-preserving mean curvature flow of rotationally symmetric surfaces
• Embeddedness of minimal surfaces with total boundary curvature at most \(4\pi\)
• Convergence of axially symmetric volume-preserving mean curvature flow
• Mean curvature flow through singularities for surfaces of rotation
• A proof of the regularity everywhere of the classical solution to Plateau's problem
• Embedded plateau problem
• Boundary regularity and embedded solutions for the oriented Plateau problem
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