The length of a shortest closed geodesic on a surface of finite area
The length of a shortest closed geodesic on a surface of finite area
In this paper we prove new upper bounds for the length of a shortest closed geodesic, denoted $l(M)$, on a complete, non-compact Riemannian surface $M$ of finite area $A$. We will show that $l(M) \leq 4\sqrt {2A}$ on a manifold with one end, thus improving the prior estimate of C. …