Generic density of geodesic nets

• Yevgeny Liokumovich ^[1] ; Bruno Staffa ^[1]
  1. [1] University of Toronto

     University of Toronto

     Canadá

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 1, 2024, págs. 2-10
• Idioma: inglés
• Enlaces
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• Resumen

  • A weighted multraph is a finite one-dimensional simplicial complex with a multiplicity n(E) ∈ N assigned to each edge (1-dimensional face) E of . A geodesic net is a map from a weighted multigraph to a Riemannian manifold (M, g), whose edges are geodesic segments in M. A geodesic net is called stationary if it is a critical point of the length functional Lg with respect to g. This is equivalent to the condition that the sum of the inward pointing unit tangent vectors (with multiplicity) is zero at every vertex (see [19] for background on stationary geodesic nets and open problems). In this paper we prove the following result.