English

A geometric approach to second-order differentiability of convex functions

Classical Analysis and ODEs 2023-08-02 v2 Differential Geometry

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 C1,1C^{1,1} convex functions and convex bodies.

Keywords

Cite

@article{arxiv.2303.06265,
  title  = {A geometric approach to second-order differentiability of convex functions},
  author = {Daniel Azagra and Anthony Cappello and Piotr Hajłasz},
  journal= {arXiv preprint arXiv:2303.06265},
  year   = {2023}
}
R2 v1 2026-06-28T09:11:50.715Z