Geodesic nets on the Euclidean plane and closed geodesic nets on Euclidean surfaces

Ivan Frolov, Denis Gorodkov, Dmitrii Korshunov +1

We prove that if $M$ is a closed Riemannian surface of diameter $d$ and area $v$ with sectional curvature in the $[-1,1]$ interval, then a closed geodesic net of length $l$ has at…