Expansion of embedded curves with turning angle greater than \(-\pi\)

DOI10.1007/s002220050034zbMath0858.53001OpenAlexW4252401661MaRDI QIDQ1922546

Lii-Perng Liou, Bennett Chow, Dong-Ho Tsai

Publication date: 26 November 1996

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/144353

zbMATH Keywords

expansioncurvature flowembedded curves

Mathematics Subject Classification ID

Initial value problems for second-order parabolic equations (35K15) Curves in Euclidean and related spaces (53A04) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (11)

Inverse curvature flows in Riemannian warped products ⋮ Snapshots of non-local constrained mean curvature-type flows ⋮ Aleksandrov reflection for extrinsic geometric flows of Euclidean hypersurfaces ⋮ Starshaped sets ⋮ DEFORMING A STARSHAPED CURVE INTO A CIRCLE BY AN AREA-PRESERVING FLOW ⋮ On a simple maximum principle technique applied to equations on the circle ⋮ Using Aleksandrov reflection to estimate the location of the center of expansion ⋮ Evolving a convex closed curve to another one via a length-preserving linear flow ⋮ Contracting convex immersed closed plane curves with slow speed of curvature ⋮ Asymptotic closeness to limiting shapes for expanding embedded plane curves ⋮ Asymptotic behavior of the isoperimetric deficit for expanding convex plane curves

Cites Work

• On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures
• Geometric expansion of convex plane curves
• Flow by mean curvature of convex surfaces into spheres
• On the formation of singularities in the curve shortening flow
• Flow of nonconvex hypersurfaces into spheres
• The heat equation shrinking convex plane curves
• The heat equation shrinks embedded plane curves to round points
• An expansion of convex hypersurfaces
• Parabolic equations for curves on surfaces. II: Intersections, blow-up and generalized solutions
• Parabolic equations for curves on surfaces. I: Curves with \(p\)-integrable curvature
• Geometric aspects of Aleksandrov reflection and gradient estimates for parabolic equations
• Contraction of convex hypersurfaces by their affine normal
• Geometric expansion of starshaped plane curves
• The zero set of a solution of a parabolic equation.
• On the affine heat equation for non-convex curves
• Aleksandrov reflection and geometric evolution of hypersurfaces

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