## Journal of the Mathematical Society of Japan

### Compression theorems for surfaces and their applications

Nobuhiro INNAMI

#### Abstract

Let $M$ be a complete glued surface whose sectional curvature is greater than or equal to $k$ and $\triangle pqr$ a geodesic triangle domain with vertices $p, q, r$ in $M$. We prove a compression theorem that there exists a distance nonincreasing map from $\triangle pqr$ onto the comparison triangle domain $\widetilde \triangle pqr$ 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

#### 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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