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A synthetic characterization of the hemisphere
Author(s):
Christopher
B.
Croke
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1083-1086.
MSC (2000):
Primary 53C22
Posted:
November 23, 2007
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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.
References:
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- C. Croke, Some isoperimetric inequalities and eigenvalue estimates, Ann. Scient. Ec. Norm. Sup., 4e serie, t.13(1980), 419-435. MR 608287 (83d:58068)
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- A. Weil, Sur les surfaces à courbure negative, C.R.A.S. 182 (1926), 1069-1071.
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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:
10.1090/S0002-9939-07-09196-4
PII:
S 0002-9939(07)09196-4
Received by editor(s):
January 23, 2007
Posted:
November 23, 2007
Additional Notes:
Supported by NSF grants DMS 02-02536 and 07-04145
Communicated by:
Jon G. Wolfson
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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