A lower bound on the quantitative version of the transversality theorem
A lower bound on the quantitative version of the transversality theorem
复制标题
DOI：
10.1016/j.jmaa.2023.127539
复制
发表时间：
2023-01
影响因子：
1.3
通讯作者：
A. Murdza;K. Nguyen
中科院分区：
文献类型：
--
作者：
A. Murdza;K. Nguyen
本文对横截性定理的定量形式给出了一个较低的估计。更精确地说，给定一个连续函数f：[0，1] d→ Rm和一个p维光滑流形W <$Rm，用幂函数的形式证明了[11]中关于ZW f <${x∈[0，1] d：f（x）∈ W}的（d+ p-m）维Hausdorff测度上界的一个清晰结果.
The present paper establishes a lower estimate on the quantitative version of the transversality theorem. More precisely, given a continuous function f:[0, 1] d→ R m and a smooth manifold W⊂ R m of dimension p, a sharpness result on the upper quantitative bound of the (d+ p− m)-dimensional Hausdorff measure of Z W f≐{x∈[0, 1] d: f (x)∈ W}, which was achieved in [11], will be proved in terms of power functions.