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 convex functions and convex bodies.
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}
}