Long-term Behavior of Curve Shortening Flow in $\mathbb{R}^3$

DOI10.1137/19M1248522zbMath1435.53067MaRDI QIDQ5220418

Jiří Minarčík, Michal Beneš

Publication date: 20 March 2020

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

zbMATH Keywords

nonlinear parabolic equationslong-term behaviorcurvature flowcurve shortening flowspace curvesspherical curvesconvex curvesavoidance principlecodimension-two problemGrayson theorem

Mathematics Subject Classification ID

Curves in Euclidean and related spaces (53A04) Flows related to mean curvature (53E10)

Related Items (2)

Qualitative and Numerical Aspects of a Motion of a Family of Interacting Curves in Space ⋮ Minimal surface generating flow for space curves of non-vanishing torsion

Cites Work

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• The theorem of Schur in the Minkowski plane
• Flow by mean curvature of convex surfaces into spheres
• The heat equation shrinking convex plane curves
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• The heat equation shrinks embedded plane curves to round points
• Level set approach to mean curvature flow in arbitrary codimension
• Singularities of the curve shrinking flow for space curves
• Shortening space curves and flow through singularities
• Comparing motion of curves and hypersurfaces in \(\mathbb{R}^m\)
• Models of phase transitions
• Application of a curvature adjusted method in image segmentation
• Four Vertices of a Convex Space Curve
• The zoo of solitons for curve shortening in $\mathbb{R}^n$
• Formation of dynamic particle accumulation structures in oscillatory thermocapillary flow in liquid bridges
• Motion of curves in three spatial dimensions using a level set approach

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