I am obviously not familiar with differential geometry. But some times I do want to know detailed answers to the following questions? May someone help?
When will there be a longest simple closed geodesic on a metric space? Of course, this is too general a question. To be more touchable, what is the case for Riemannian manifolds with non-positive curvature?
Or more generally is there any reference for the the relationship between longest/shortest simple closed curve, diameter, area and curvature?