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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A synthetic characterization of the hemisphere


Author: Christopher B. Croke
Journal: Proc. Amer. Math. Soc. 136 (2008), 1083-1086
MSC (2000): Primary 53C22
Published electronically: November 23, 2007
MathSciNet review: 2361884
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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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Additional Information

Christopher B. Croke
Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395
Email: ccroke@math.upenn.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09196-4
PII: S 0002-9939(07)09196-4
Received by editor(s): January 23, 2007
Published electronically: November 23, 2007
Additional Notes: Supported by NSF grants DMS 02-02536 and 07-04145
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.