Let $S$ be a surface of nonpositive curvature of genus bigger than 1 (i.e. not the torus). We prove that any flat strip in the surface is in fact a flat cylinder. Moreover we prove that the number of homotopy classes of such flat cylinders is bounded.
Phase transitions for the geodesic flow of a rank one surface with nonpositive curvature
On the ergodicity of geodesic flows on surfaces of nonpositive curvature
Counterexamples in nonpositive curvature
![QR code for arXiv:math/0301010 [math.DS]](http://oss.arxitics.com/images/favicon.svg)