Area growth and rigidity of surfaces without conjugate points
Victor Bangert, Patrick Emmerich
TL;DR
This paper proves that complete Riemannian planes and cylinders without conjugate points are flat if they satisfy certain optimal area growth conditions, advancing understanding of geometric rigidity.
Contribution
It establishes flatness of such surfaces under optimal area growth conditions, extending previous rigidity results.
Findings
Complete Riemannian planes without conjugate points are flat under area growth conditions.
Complete Riemannian cylinders without conjugate points are flat under area growth conditions.
The results are optimal, meaning the conditions cannot be weakened further.
Abstract
We prove flatness of complete Riemannian planes and cylinders without conjugate points under optimal conditions on the area growth.
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