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A synthetic characterization of the hemisphere

Christopher B. Croke
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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.

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Christopher B. Croke. 2004-06-14. A synthetic characterization of the hemisphere. https://arxiv.org/abs/math/0406283

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