A geometric approach to second-order differentiability of convex functions

2023/03/11 by Daniel Azagra, Azagra, Daniel, Anthony Cappello +3 · 1 citation
Computer Science · Mathematics · #26B25 #28A75 #41A30 #52A20 #52A27 #53C45 #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Functional Equations Stability Results #Mathematics and Applications #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2303.06265

openalex publication_date 2023/03/11 · openalex created_date 2023/03/16 · openalex updated_date 2026/07/28

Abstract

We show a new, elementary and geometric proof of the classical Alexandrov theorem about the second order differentiability of convex functions. We also show new proofs of recent results about Lusin approximation of convex functions and convex bodies by C^1,1 convex functions and convex bodies.

Cited by

• C²-Lusin approximation of convex functions: one variable case

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