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July, 2007 Compression theorems for surfaces and their applications
Nobuhiro INNAMI
J. Math. Soc. Japan 59(3): 825-835 (July, 2007). DOI: 10.2969/jmsj/05930825


Let M be a complete glued surface whose sectional curvature is greater than or equal to k and p q r a geodesic triangle domain with vertices p , q , r in M . We prove a compression theorem that there exists a distance nonincreasing map from p q r onto the comparison triangle domain ˜ p q r in the two-dimensional space form with sectional curvature k . Using the theorem, we also have some compression theorems and an application to a circular billiard ball problem on a surface.


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Nobuhiro INNAMI. "Compression theorems for surfaces and their applications." J. Math. Soc. Japan 59 (3) 825 - 835, July, 2007.


Published: July, 2007
First available in Project Euclid: 5 October 2007

zbMATH: 1129.53035
MathSciNet: MR2344830
Digital Object Identifier: 10.2969/jmsj/05930825

Primary: 53C20
Secondary: 53C22

Keywords: Alexandrov space , compression theorem , Geodesic

Rights: Copyright © 2007 Mathematical Society of Japan


Vol.59 • No. 3 • July, 2007
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