  What are appropriate geometric conditions ensuring that a complete Riemannian
2-cylinder without conjugate points is flat? Examples with nonpositive
curvature show that one has to assume that the ends of the cylinder open
sublinearly. We show that sublinear growth of the ends is indeed sufficient if
it is measured by the length of horocycles. This is used to extend results by
K. Burns and G. Knieper [9], and by H. Koehler [18], where the opening of the
ends is measured in terms of shortest noncontractible loops.
