A geometric approach to second-order differentiability of convex functions

DOI10.1090/bproc/190arXiv2303.06265OpenAlexW4388098014MaRDI QIDQ6066397

Piotr Hajłasz, Unnamed Author, Daniel Azagra

Publication date: 16 November 2023

Published in: Proceedings of the American Mathematical Society, Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.06265

zbMATH Keywords

convex functionconvex bodyLusin propertyAlexandrov theoremLipschitz gradient

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Convexity of real functions of several variables, generalizations (26B25) Approximation by other special function classes (41A30) Approximation by convex sets (52A27) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Cites Work

• Locally \(C^{1,1}\) convex extensions of \(1\)-jets
• On the inner parallel body of a convex body
• Global geometry and \(C^1\) convex extensions of 1-jets
• Explicit formulas for \(C^{1,1}\) and \(C_{\operatorname{conv}}^{1, \omega}\) extensions of 1-jets in Hilbert and superreflexive spaces
• On the second differentiability of convex surfaces
• Regularity classes for operations in convexity theory
• Lusin-type properties of convex functions and convex bodies
• Differentiability of convex envelopes
• Global and fine approximation of convex functions
• Whitney extension theorems for convex functions of the classes C1 and C1,ω
• Convex Bodies The Brunn-MinkowskiTheory
• Notions of convexity
• Unnamed Item

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