Motion by curvature of planar networks II

• Annibale Magni ^[2] ; Carlo Mantegazza ^[3] ; Matteo Novaga ^[1]
  1. [1] University of Pisa

     University of Pisa

     Pisa, Italia

     
  2. [2] Universität Münster, Germany
  3. [3] Università di Napoli “Federico II”, Italia

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• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 15, Nº Extra 1 (Special volume), 2016, págs. 117-144
• Idioma: inglés
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• Resumen

  • 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 as long as 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.