For a two-dimensional convex body, the Kovner-Besicovitch measure of symmetry is defined as the volume ratio of the largest centrally symmetric body contained inside the body to the original body. A classical result states that the Kovner-Besicovitch measure is at least $2/3$ for every convex body and equals $2/3$ for triangles. Lassak showed that an alternative measure of symmetry, i.e., symmetry about a line (axiality) has a value of at least $2/3$ for every convex body. However, the smallest known value of the axiality of a convex body is around $0.81584$, achieved by a convex quadrilateral. We show that every plane convex body has axiality at least $\frac{2}{41}(10 + 3 \sqrt{2}) \approx 0.69476$, thereby establishing a separation with the central symmetry measure. Moreover, we find a family of convex quadrilaterals with axiality approaching $\frac{1}{3}(\sqrt{2}+1) \approx 0.80474$. We also establish improved bounds for a ``folding" measure of axial symmetry for plane convex bodies. Finally, we establish improved bounds for a generalization of axiality to high-dimensional convex bodies.

翻译：对于二维凸体，Kovner-Besicovitch 对称性度量定义为包含在该凸体内的最大中心对称体与该凸体本身的体积比。一个经典结论指出，每个凸体的 Kovner-Besicovitch 度量至少为 $2/3$，且三角形恰好达到该值 $2/3$。Lassak 展示了另一种对称性度量，即关于直线的对称性（轴对称性），对每个凸体其值至少为 $2/3$。然而，目前已知凸体轴对称性的最小值为某个凸四边形所达到的约 $0.81584$。我们证明每个平面凸体的轴对称性至少为 $\frac{2}{41}(10 + 3 \sqrt{2}) \approx 0.69476$，从而建立了与中心对称性度量的分离。此外，我们找到了一族凸四边形，其轴对称性趋近于 $\frac{1}{3}(\sqrt{2}+1) \approx 0.80474$。我们还针对平面凸体的“折叠”型轴对称性度量给出了改进的界。最后，我们针对轴对称性到高维凸体的推广形式建立了改进的界。