Generic density of stationary geodesic nets that are not closed geodesics

2025/10/02 by Talant Talipov, Talipov, Talant
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Morphological variations and asymmetry

paper · pdf · doi:10.48550/arxiv.2510.02588

openalex publication_date 2025/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for a Baire-generic Riemannian metric on a closed smooth manifold of dimension greater than or equal 3, the union of stationary geodesic nets that are not closed geodesics forms a dense set. This result confirms a Nabutovsky-Parsch conjecture in this case.

Citations

• Weyl law for 1-cycles
• On the equidistribution of closed geodesics and geodesic nets
• Stable geodesic nets in convex hypersurfaces
• Generic density of geodesic nets
• Bumpy Metrics Theorem for Geodesic Nets
• Geodesic Nets: Some Examples and Open Problems
• Equidistribution of minimal hypersurfaces for generic metrics
• Density of minimal hypersurfaces for generic metrics

Related

• Generic density of geodesic nets
• Bumpy Metrics Theorem for Geodesic Nets
• Random 3-Manifolds Have No Totally Geodesic Submanifolds
• Density of minimal hypersurfaces for generic metrics
• On the equidistribution of closed geodesics and geodesic nets