A sharp quantitative estimate of critical sets

2024/05/27 by Andrew Murdza, Murdza, Andrew, Khai T. Nguyen +1
Mathematics · #46T20 #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results

paper · pdf · doi:10.48550/arxiv.2405.17107

openalex publication_date 2024/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper establishes a sharp quantitative estimate for the (d-1)-Hausdorff measure of the critical set of C¹ vector-valued functions on ℝ^d. Additionally, we prove that for a generic C² function where ``generic" is understood in the topological sense of Baire category, the critical set has a locally finite (d-1)-Hausdorff measure.

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