3 papers
math.DG2026
The Shortest Geodesic Flower on a Manifold with Locally Convex Ends and Finite Volume
Isabel Beach
Suppose is a complete, non-compact -dimensional Riemannian manifold with locally convex ends and finite volume. We prove that admits a non-trivial geodesic net with one…
math.DG2025
Short Simple Geodesic Loops on a 2-Sphere
Isabel Beach
The classic Lusternik--Schnirelmann theorem states that there are three distinct simple periodic geodesics on any Riemannian 2-sphere . It has been proven by Y. Liokumovich, A.…
math.DG2025
Short Simple Orthogonal Geodesic Chords on a 2-Disk with Convex Boundary
Isabel Beach
We prove the existence of at least two distinct short, simple orthogonal geodesic chords on a Riemannian 2-disk with convex boundary. The lengths of these curves are bounded in…