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.
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