arXiv:2303.06265 Abstract | arXiv Analytics

arXiv:2303.06265 [math.CA]Abstract References Reviews Resources

A geometric approach to second-order differentiability of convex functions

Daniel Azagra, Anthony Cappello, Piotr Hajłasz

Published 2023-03-11, updated 2023-07-31Version 2

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.

Categories: math.CA, math.DG

Subjects: 26B25, 28A75, 41A30, 52A20, 52A27, 53C45

Keywords: convex functions, geometric approach, second-order differentiability, convex bodies, second order differentiability

Related articles: Most relevant | Search more

arXiv:1112.3976 [math.CA] (Published 2011-12-16)

Non-uniqueness of convex bodies with prescribed volumes of sections and projections

Fedor Nazarov, Dmitry Ryabogin, Artem Zvavitch

arXiv:2311.00912 [math.CA] (Published 2023-11-02)

Whitney-type estimates for convex functions

Andriy Prymak, Jaskaran Singh

arXiv:math/0504567 [math.CA] (Published 2005-04-28, updated 2005-09-20)

Convex functions with unbounded gradient