Logarithmic systolic growth for hyperbolic surfaces in every genus

More than thirty years ago, Brooks J. Reine Angew. Math. 390 (1988), pp. 117–129 and Buser–Sarnak Invent. Math. 117 (1994), pp. 27–56 constructed sequences of closed hyperbolic surfaces with logarithmic systolic growth in the genus. Recently, Liu and Petri Random surfaces with large systoles, https://arxiv.org/abs/2312.11428, 2023 showed that such logarithmic systolic lower bound holds for every genus (not merely for genera in some infinite sequence) using random surfaces. In this article, we show a similar result through a more direct approach relying on the original Brooks/Buser–Sarnak surfaces.