Loss of convexity and embeddedness for geometric evolution equations of higher order

DOI10.1007/s00028-009-0038-2zbMath1239.53082OpenAlexW2013866230MaRDI QIDQ423392

Simon Blatt

Publication date: 2 June 2012

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/11858/00-001M-0000-0013-60AD-B

zbMATH Keywords

nonlinear parabolic equationsgeometric evolution equations

Mathematics Subject Classification ID

Related Items (8)

The polyharmonic heat flow of closed plane curves ⋮ On the curve diffusion flow of closed plane curves ⋮ Li-Yau type inequality for curves in any codimension ⋮ Surface diffusion flow near spheres ⋮ On the isoperimetric inequality and surface diffusion flow for multiply winding curves ⋮ The gradient flow of the Möbius energy near local minimizers ⋮ Stability of geometric flows on the circle ⋮ Representation formulae for higher order curvature flows

Cites Work

• Flow by mean curvature of convex surfaces into spheres
• The heat equation shrinking convex plane curves
• Contraction of convex hypersurfaces in Euclidean space
• A numerical scheme for axisymmetric solutions of curvature-driven free boundary problems, with applications to the Willmore flow
• The problem of optimal smoothing for convex functions
• Self-intersections for the surface diffusion and the volume-preserving mean curvature flow
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