A synthetic characterization of the hemisphere

Details A synthetic characterization of the hemisphere A synthetic characterization of the hemisphere

2004-06-14

arxiv.org/abs/math/0406283v1

Mathematics

Differential Geometry

Latex, 4 pages

Scientific paper

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.

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