Inverse mean curvature flow for star-shaped hypersurfaces evolving in a cone

DOI10.1007/s12220-011-9288-7zbMath1317.53087OpenAlexW2074205739MaRDI QIDQ363213

Thomas Marquardt

Publication date: 2 September 2013

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/11858/00-001M-0000-0015-14AE-A

zbMATH Keywords

gradient estimatenonlinear boundary value probleminverse mean curvature flowlong time existence

Mathematics Subject Classification ID

Related Items (12)

Evolution of noncompact hypersurfaces by inverse mean curvature ⋮ Weak solutions of inverse mean curvature flow for hypersurfaces with boundary ⋮ Inverse mean curvature flow for star-shaped hypersurfaces evolving in a cone ⋮ An anisotropic inverse mean curvature flow for spacelike graphic hypersurfaces with boundary in Lorentz-Minkowski space \(\mathbb{R}^{n+1}_1\) ⋮ The Riemannian Penrose inequality for asymptotically flat manifolds with non-compact boundary ⋮ First eigenvalues of free boundary hypersurfaces in the unit ball along the inverse mean curvature flow ⋮ A mean curvature type flow with capillary boundary in a unit ball ⋮ Starshaped sets ⋮ Hyperbolic inverse mean curvature flow ⋮ Capacity inequalities and rigidity of cornered/conical manifolds ⋮ Existence of self-similar solutions of the inverse mean curvature flow ⋮ The inverse mean curvature flow perpendicular to the sphere

Cites Work

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• Inverse mean curvature flow for star-shaped hypersurfaces evolving in a cone
• On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures
• Flow of nonconvex hypersurfaces into spheres
• Higher regularity of the inverse mean curvature flow
• The inverse mean curvature flow and the Riemannian Penrose inequality
• Proof of the Riemannian Penrose inequality using the positive mass theorem.
• Regularity estimates for solutions to the mean curvature flow with a Neumann boundary condition
• Convergence of solutions to the mean curvature flow with a Neumann boundary condition
• The Motion of a Surface by Its Mean Curvature. (MN-20)

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