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arXiv · 2303.06265

A geometric approach to second-order differentiability of convex functions

Daniel Azagra·Anthony Cappello·Piotr Hajłasz
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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.

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Daniel Azagra, Anthony Cappello, Piotr Hajłasz. 2023-03-11. A geometric approach to second-order differentiability of convex functions. https://arxiv.org/abs/2303.06265

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