Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 59, Number 3 (2007), 825-835.
Compression theorems for surfaces and their applications
Let be a complete glued surface whose sectional curvature is greater than or equal to and a geodesic triangle domain with vertices in . We prove a compression theorem that there exists a distance nonincreasing map from onto the comparison triangle domain in the two-dimensional space form with sectional curvature . Using the theorem, we also have some compression theorems and an application to a circular billiard ball problem on a surface.
J. Math. Soc. Japan, Volume 59, Number 3 (2007), 825-835.
First available in Project Euclid: 5 October 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 53C22: Geodesics [See also 58E10]
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