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math.DS2025
Closed geodesics and the first Betti number
Gonzalo Contreras, Marco Mazzucchelli
We prove that, on any closed manifold of dimension at least two with non-trivial first Betti number, a generic Riemannian metric has infinitely many closed geodesics, an…
math.DS2025
From curve shortening to flat link stability and Birkhoff sections of geodesic flows
Marcelo R. R. Alves, Marco Mazzucchelli
We employ the curve shortening flow to establish three new results on the dynamics of geodesic flows of closed Riemannian surfaces. The first one is the stability, under -smal…