A lower bound on the quantitative version of the transversality theorem

2023/01/01 by Murdza, Andrew, Nguyen, Khai T.
#46T20 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2301.00432

Abstract

The present paper studies a quantitative version of the transversality theorem. More precisely, given a continuous function f∈ C([0,1]^d,ℝ^m) and a manifold W⊂ ℝ^m of dimension p, a sharpness result on the upper quantitative estimate of the (d+p-m)-dimensional Hausdorff measure of the set Z_W^f=\x∈ [0,1]^d: f(x)∈ W\, which was achieved in [8], will be proved in terms of power functions.

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