Area-preserving anisotropic mean curvature flow in two dimensions

DOI10.1007/S00526-024-02859-6MaRDI QIDQ6657164

Dohyun Kwon, Eric S. Kim

Publication date: 6 January 2025

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

zbMATH Keywords

Wulff shapearea-preserving anisotropic mean curvature flowCahn-Hoffman mapreflection comparison symmetries preservation

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Long-time behavior of solutions for dynamical problems in solid mechanics (74H40) Flows related to mean curvature (53E10)

Cites Work

• Global solutions to the volume-preserving mean-curvature flow
• Nonlocal curvature flows
• The volume preserving crystalline mean curvature flow of convex sets in \(\mathbb R^N\)
• Regularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals
• Implicit time discretization for the mean curvature flow equation
• Uniqueness problem for closed non-smooth hypersurfaces with constant anisotropic mean curvature and self-similar solutions of anisotropic mean curvature flow
• Volume preserving mean curvature flow for star-shaped sets
• Uniqueness of critical points of the anisotropic isoperimetric problem for finite perimeter sets
• Dynamic stability of equilibrium capillary drops
• Regularity theory for elliptic PDE
• A Singular Example for the Averaged Mean Curvature Flow
• Sets of finite perimeter and geometric variational problems. An introduction to geometric measure theory
• Volume preserving anisotropic mean curvature flow
• Geometry and Materials
• Curvature-Driven Flows: A Variational Approach
• On mean curvature flow with forcing
• The existence of a weak solution to volume preserving mean curvature flow in higher dimensions
• The asymptotics of the area-preserving mean curvature and the Mullins-Sekerka flow in two dimensions

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