In response to Sanki-Vadnere, we present a short proof of the following theorem: a pair of simple curves on a hyperbolic surface whose complementary regions are disks has length at least half the perimeter of the regular right-angled $(8g-4)$-gon.

中文翻译：

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奥加布-黄猜想的简短证明

作为对 Sanki-Vadnere 的回应，我们提出了以下定理的简短证明：互补区域是圆盘的双曲曲面上的一对简单曲线的长度至少是规则直角 $(8g-4) 周长的一半$-gon。