We prove that on a closed 3-manifold with $sec\ge k$ and $diam\le D$
the length of the shortest closed geodesic is $\le C(k,D)$.
This is joint work with R. Rotman.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3050