Area growth and rigidity of surfaces without conjugate points
We prove flatness of complete Riemannian planes and cylinders without conjugate points under optimal conditions on the area growth.
math.DG↗
arXiv subjects
Patrick Emmerich
Publications and source records attributed to Patrick Emmerich.
On the flatness of Riemannian cylinders without conjugate points
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.
math.DG↗