C²-Lusin approximation of strongly convex bodies

2024/07/08 by Daniel Azagra, Azagra, Daniel, Marjorie Drake +3 · 1 citation
Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2407.05745

openalex publication_date 2024/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that, if W ⊂ ℝⁿ is a locally strongly convex body (not necessarily compact), then for any open set V ⊃ ∂ W and ε>0, and V ⊃ ∂ W is open, then there exists a C² locally strongly convex body W_{ε, V} such that H^n-1(∂ W_{ε, V}\triangle ∂ W)<ε and ∂ W_{ε, V}⊂ V. Moreover, if W is strongly convex, then W_{ε, V} is strongly convex as well.

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