For any e>0, we construct a closed hyperbolic surface of genus g=g(e) with a set of at most eg systoles that fill, meaning that each component of the complement of their union is contractible. This surface is also a critical point of index at most eg for the systole function, disproving the lower bound of 2g−1 conjectured by Schmutz Schaller.

中文翻译：

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具有亚线性许多收缩期的双曲曲面填充

对于任何 e>0，我们构造一个 g=g(e) 属的闭合双曲曲面，其中最多有一组填充，例如，收缩期，这意味着它们联合的补集的每个分量都是可收缩的。该表面也至多是指数的临界点，例如对于收缩功能，反驳了 Schmutz Schaller 推测的 2g-1 的下界。