Whitney extension theorems for convex functions of the classes C1 and C1,ω

DOI10.1112/plms.12006zbMath1379.54014arXiv1507.03931OpenAlexW2964089210MaRDI QIDQ5357203

Carlos Mudarra, Daniel Azagra

Publication date: 14 September 2017

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.03931

zbMATH Keywords

modulus of continuityconvex functionsWhitney extension theorems\(\omega\)-Lipschitz

Mathematics Subject Classification ID

Convex functions and convex programs in convex geometry (52A41) Continuity and differentiation questions (26B05) Extension of maps (54C20) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Differentiable maps on manifolds (58C25) Classical differential geometry (53A99) Monge-Ampère equations (35J96)

Related Items (17)

Locally \(C^{1,1}\) convex extensions of \(1\)-jets ⋮ Global geometry and \(C^1\) convex extensions of 1-jets ⋮ Explicit formulas for 𝐶^{1,1} Glaeser-Whitney extensions of 1-Taylor fields in Hilbert spaces ⋮ Lusin-type properties of convex functions and convex bodies ⋮ Smooth convex extensions of convex functions ⋮ A geometric approach to second-order differentiability of convex functions ⋮ On L^p Markov type inequality for some cuspidal domains ⋮ Explicit formulas for \(C^{1,1}\) and \(C_{\operatorname{conv}}^{1, \omega}\) extensions of 1-jets in Hilbert and superreflexive spaces ⋮ Convex \(C^1\) extensions of \(1\)-jets from compact subsets of Hilbert spaces ⋮ Self-contracted curves are gradient flows of convex functions ⋮ Extensions of convex functions with prescribed subdifferentials ⋮ Whitney differentiability of optimal-value functions for bound-constrained convex programming problems ⋮ Prescribing tangent hyperplanes to $C^{1,1}$ and $C^{1,\omega}$ convex hypersurfaces in Hilbert and superreflexive Banach spaces ⋮ \(C^{1, \omega }\) extension formulas for $1$-jets on Hilbert spaces ⋮ Minimizers of convex functionals with small degeneracy set ⋮ On the global shape of continuous convex functions on Banach spaces ⋮ Kirszbraun’s Theorem via an Explicit Formula

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