Generic density of geodesic nets

TL;DR

This paper proves that for a generic Riemannian metric on a closed manifold, the combined images of all stationary geodesic nets are dense, highlighting a generic geometric property.

Contribution

It establishes that the union of stationary geodesic nets is dense for a Baire-generic set of Riemannian metrics, a novel genericity result in differential geometry.

Findings

Union of stationary geodesic nets is dense for generic metrics

Density holds for Baire-generic Riemannian metrics

Advances understanding of geodesic net distribution

Abstract

We prove that for a Baire-generic Riemannian metric on a closed smooth manifold, the union of the images of all stationary geodesic nets forms a dense set.