A Singular Example for the Averaged Mean Curvature Flow

DOI10.1080/10586458.2001.10504432zbMath0982.53061OpenAlexW2098947073MaRDI QIDQ2729381

Uwe F. Mayer

Publication date: 22 July 2001

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/228798

zbMATH Keywords

singularitycurveself-intersectionaveraged mean curvature flowblowup of curvature

Mathematics Subject Classification ID

Related Items (18)

Long time behavior of discrete volume preserving mean curvature flows ⋮ Optimal control of volume-preserving mean curvature flow ⋮ An application of interpolation inequalities between the deviation of curvature and the isoperimetric ratio to the length-preserving flow ⋮ AN AREA-PRESERVING FLOW FOR CLOSED CONVEX PLANE CURVES ⋮ Singularities of the area preserving curve shortening flow with a free boundary condition ⋮ Global stability of traveling waves for an area preserving curvature flow with contact angle condition ⋮ Theory and numerics for Chen's flow of curves ⋮ Star-shaped centrosymmetric curves under Gage's area-preserving flow ⋮ The asymptotics of the area-preserving mean curvature and the Mullins-Sekerka flow in two dimensions ⋮ Nonlocal estimates for the volume preserving mean curvature flow and applications ⋮ 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 ⋮ A fully Lagrangian meshfree framework for PDEs on evolving surfaces ⋮ DEFORMING A STARSHAPED CURVE INTO A CIRCLE BY AN AREA-PRESERVING FLOW ⋮ Optimal unstirred state of a passive scalar ⋮ On a non-local perimeter-preserving curve evolution problem for convex plane curves ⋮ Some dynamic properties of volume preserving curvature driven flows

Cites Work

• On the formation of singularities in the curve shortening flow
• The heat equation shrinks embedded plane curves to round points
• The volume preserving mean curvature flow near spheres
• A numerical scheme for moving boundary problems that are gradient flows for the area functional
• The Surface Evolver

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