In this note we study caustic-free regions for convex billiard tables in the hyperbolic plane or the hemisphere. In particular, following a result by Gutkin and Katok in the Euclidean case, we estimate the size of such regions in terms of the geometry of the billiard table. Moreover, we extend to this setting a theorem due to Hubacher which shows that no caustics exist near the boundary of a convex billiard table whose curvature is discontinuous.

中文翻译：

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等曲率表面台球的无焦散区域

在本笔记中，我们研究了双曲平面或半球中凸台球桌的无焦散区域。特别是，根据 Gutkin 和 Katok 在欧几里得情况下的结果，我们根据台球桌的几何形状估计这些区域的大小。此外，我们将 Hubacher 的定理扩展到这个设置，该定理表明在曲率不连续的凸台球桌的边界附近不存在焦散。