We give sharp upper bounds on the injectivity radii of complete hyperbolic surfaces of finite area with some geodesic boundary components. The given bounds are over all such surfaces with any fixed topology; in particular, boundary lengths are not fixed. This extends the first author’s earlier result to the with-boundary setting. In the second part of the paper we comment on another direction for extending this result, via the systole of loops function.

中文翻译：

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具有测地线边界的双曲曲面的最大注入半径

我们给出了具有一些测地边界分量的有限区域的完整双曲曲面的注入半径的尖锐上限。给定的边界在所有具有任何固定拓扑结构的表面上；特别是，边界长度不是固定的。这将第一作者的早期结果扩展到带边界设置。在论文的第二部分，我们通过循环功能的收缩对扩展这个结果的另一个方向进行了评论。