Motion by curvature of planar networks II

Annibale Magni; Carlo Mantegazza; Matteo Novaga

Motion by curvature of planar networks II

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arxiv 1301.3352 v2 pith:EEAIFFEG submitted 2013-01-15 math.AP math.DG

Annibale Magni , Carlo Mantegazza , Matteo Novaga This is my paper · ORCID

classification math.APmath.DG

keywords threecurvaturecurvesendpointsexistsnetworkplanartimes

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We prove that the curvature flow of an embedded planar network of three curves connected through a triple junction, with fixed endpoints on the boundary of a given strictly convex domain, exists smooth until the lengths of the three curves stay far from zero. If this is the case for all times, then the evolution exists for all times and the network converges to the Steiner minimal connection between the three endpoints.

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