A synthetic characterization of the hemisphere
Differential Geometry
2007-05-23 v1 Metric Geometry
Abstract
We show that round hemispheres are the only compact 2 dimensional Riemannian manifolds (with or without boundary) such that almost every pair of complete geodesics intersect once and only once. We prove this by establishing a sharp isoperimetric inequality for surfaces with boundary such that every pair of geodesics have at most one interior intersection point.
Cite
@article{arxiv.math/0406283,
title = {A synthetic characterization of the hemisphere},
author = {Christopher B. Croke},
journal= {arXiv preprint arXiv:math/0406283},
year = {2007}
}
Comments
Latex, 4 pages