Long time behavior of discrete volume preserving mean curvature flows

DOI10.1515/crelle-2021-0076zbMath1496.53098arXiv2004.04799OpenAlexW4207054141MaRDI QIDQ2121385

Massimiliano Morini, Marcello Ponsiglione, Emanuele Nunzio Spadaro

Publication date: 4 April 2022

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.04799

zbMATH Keywords

stationary setsconvergence of the barycentersnearly spherical setsquantitative Alexandrov theorem

Mathematics Subject Classification ID

Polyhedral manifolds (52B70) Flows related to mean curvature (53E10) Discrete differential geometry (53A70)

Related Items (8)

Global and local energy minimizers for a nanowire growth model ⋮ The asymptotics of the area-preserving mean curvature and the Mullins-Sekerka flow in two dimensions ⋮ Asymptotic of the discrete volume-preserving fractional mean curvature flow via a nonlocal quantitative Alexandrov theorem ⋮ Stability of the ball under volume preserving fractional mean curvature flow ⋮ Long time behaviour of the discrete volume preserving mean curvature flow in the flat torus ⋮ Quantitative Alexandrov theorem and asymptotic behavior of the volume preserving mean curvature flow ⋮ Consistency of the flat flow solution to the volume preserving mean curvature flow ⋮ Unnamed Item

Cites Work

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• Global solutions to the volume-preserving mean-curvature flow
• Minimality via second variation for a nonlocal isoperimetric problem
• Isoperimetry with upper mean curvature bounds and sharp stability estimates
• On periodic critical points and local minimizers of the Ohta-Kawasaki functional
• The volume preserving crystalline mean curvature flow of convex sets in \(\mathbb R^N\)
• Implicit time discretization for the mean curvature flow equation
• A sharp quantitative version of Alexandrov's theorem via the method of moving planes
• Bubbling with \(L^2\)-almost constant mean curvature and an Alexandrov-type theorem for crystals
• Volume preserving mean curvature flow for star-shaped sets
• Volume preserving mean curvature flows near strictly stable sets in flat torus
• Alexandrov's theorem revisited
• A Singular Example for the Averaged Mean Curvature Flow
• Sets of Finite Perimeter and Geometric Variational Problems
• An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs
• On the Shape of Compact Hypersurfaces with Almost-Constant Mean Curvature
• The volume preserving mean curvature flow.
• The volume preserving mean curvature flow near spheres
• Curvature-Driven Flows: A Variational Approach
• On the Coarsening Rates for Attachment-Limited Kinetics
• Self-intersections for the surface diffusion and the volume-preserving mean curvature flow

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