Resumen de Generic density of geodesic nets

Yevgeny Liokumovich, Bruno Staffa

• 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.