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Soliton solutions for the elastic metric on spaces of curves

Presented by: 
Peter Michor Universität Wien
Thursday 14th December 2017 - 09:00 to 10:00
INI Seminar Room 1
Joint work with: Martin Bauer (Florida State University), Martins Bruveris (Brunel University London), Philipp Harms (University of Freiburg). Abstract: Some first order Sobolev metrics on spaces of curves admit soliton-like geodesics, i.e., geodesics whose momenta are sums of delta distributions. It turns out that these geodesics can be found within the submanifold of piecewise linear curves, which is totally geodesic for these metrics. Consequently, the geodesic equation reduces to a finite-dimensional ordinary differential equation for a dense set of initial conditions.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons