A synthetic characterization of the hemisphere

Croke, Christopher

doi:10.1090/S0002-9939-07-09196-4

A synthetic characterization of the hemisphere
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by Christopher B. Croke PDF

Proc. Amer. Math. Soc. 136 (2008), 1083-1086 Request permission

Abstract:

We show that round hemispheres are the only compact two-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 has at most one interior intersection point.

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