Journal of the Mathematical Society of Japan

Compression theorems for surfaces and their applications

Nobuhiro INNAMI

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Abstract

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.

Article information

Source
J. Math. Soc. Japan, Volume 59, Number 3 (2007), 825-835.

Dates
First available in Project Euclid: 5 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1191591860

Digital Object Identifier
doi:10.2969/jmsj/05930825

Mathematical Reviews number (MathSciNet)
MR2344830

Zentralblatt MATH identifier
1129.53035

Subjects
Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 53C22: Geodesics [See also 58E10]

Keywords
compression theorem geodesic Alexandrov space

Citation

INNAMI, Nobuhiro. Compression theorems for surfaces and their applications. J. Math. Soc. Japan 59 (2007), no. 3, 825--835. doi:10.2969/jmsj/05930825. https://projecteuclid.org/euclid.jmsj/1191591860


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