标题： 关于Kobayashi距离在接近$\mathcal C^2$-光滑边界点时的最优界值 显示英文标题

标题： Optimal bounds for the Kobayashi distance near $\mathcal C^2$-smooth boundary points

摘要： 结果表明，L. Kosinski、N. Nikolov、A.Y. Okten 在文章《强伪凸域上的精确不变距离估计》（Adv. Math. 478 (2025), 1100388）中得到的关于Kobayashi距离在 $\mathcal C^{2,\alpha}$-光滑强伪凸边界点附近的最优上下界，在一般的 $\mathcal C^2$ 强伪凸情形下仍然成立。事实上，上界被推广到了一般的 $\mathcal C^{1,1}$-光滑情形。我们还给出了非半正边界点附近Kobayashi距离的上下界。 显示英文摘要

摘要： It is shown that the optimal upper and lower bounds for the Kobayashi distance near $\mathcal C^{2,\alpha}$-smooth strongly pseudoconvex boundary points obtained in L. Kosinski, N. Nikolov, A.Y. Okten: "Precise estimates of invariant distances on strongly pseudoconvex domains", Adv. Math. 478 (2025), 110388, remain true in the general $\mathcal C^2$ strongly pseudoconvex setting. In fact, the upper bound is extended to the general $\mathcal C^{1,1}$-smooth case. We also give upper and lower bounds for the Kobayashi distance near non-semipositive boundary points.