Evolution of convex lens-shaped networks under the curve shortening flow

DOI10.1090/S0002-9947-2010-04820-2zbMath1220.53083arXiv0711.1108WikidataQ57535402 ScholiaQ57535402MaRDI QIDQ3003601

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Publication date: 27 May 2011

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.1108

zbMATH Keywords

mean curvature flownetworksasymptotic behaviourtriple junctionsself-similar shrinking networks

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40)

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Cites Work

• Unnamed Item
• Self-similar solutions of a 2-D multiple-phase curvature flow
• Asymptotic behavior for singularities of the mean curvature flow
• Mean curvature evolution of entire graphs
• Interior estimates for hypersurfaces moving by mean curvature
• The normalized curve shortening flow and homothetic solutions
• The heat equation shrinking convex plane curves
• The heat equation shrinks embedded plane curves to round points
• A distance comparison principle for evolving curves
• Time-interior gradient estimates for quasilinear parabolic equations
• Classification of limiting shapes for isotropic curve flows
• Sharp estimates for mean curvature flow of graphs