We improve a lower bound for the smallest area of convex covers for closed unit curves from 0.0975 to 0.1, which makes it substantially closer to the current best upper bound 0.11023. We did this by considering the minimal area of convex hull of circle, line of length $\frac{1}{2}$, and rectangle with side $0.1727\times 0.3273$. By using geometric methods and the Box-search algorithm, we proved that this area is at least 0.1. We give informal numerical evidence that the obtained lower bound is close to the limit of current techniques, and substantially new idea is required to go significantly beyond 0.10044.

中文翻译：

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用于封闭的单位曲线的凸盖的面积至少为0.1

对于封闭的单位曲线，我们将凸盖的最小面积的下限从0.0975改进为0.1，这使它实际上更接近当前的最佳上限0.11023。我们通过考虑圆的凸包的最小面积，长度的线来做到这一点$\frac{\mathrm{1个}}{2}$和带边的矩形 $0。1727\times 0。3273$。通过使用几何方法和Box-search算法，我们证明了该区域至少为0.1。我们提供非正式的数值证据，表明所获得的下界已接近当前技术的极限，并且需要实质上新的思想以大大超过0.10044。