A synthetic characterization of the hemisphere

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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.
Latex, 4 pages

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Differential Geometry, Metric Geometry, 53C22; 53C24; 53C65; 53A99; 53C20

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http://salesiana.dossiersoluciones.com/handle/123456789/71554

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0406283
 http://arxiv.org/abs/math/0406283

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arXiv