University of Cambridge > Talks.cam > Geometric Analysis and Partial Differential Equations seminar > On short time existence of the network flow.

On short time existence of the network flow.

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  • UserFelix Schulze (Free University, Berlin)
  • ClockMonday 21 March 2011, 16:00-17:00
  • HouseCMS, MR15.

If you have a question about this talk, please contact Prof. Neshan Wickramasekera.

I will report on joint work with T. Ilmanen and A. Neves on how to prove the existence of an embedded, regular network moving by curve shortening flow in the plane, starting from a non-regular initial network. Here a regular network consists of smooth, embedded line-segments such that at each endpoint, if not infinity, there are three arcs meeting under a 120 degree angle. In the non-regular case we allow that an arbitrary number of line segments meet at an endpoint, without an angle condition. The proof relies on gluing in appropriately scaled self-similarly expanding solutions and a new monotonicity formula, together with a local regularity result for such evolving networks. This short time existence result also has applications in extending such a flow of networks through singularities.

This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.

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