Lipschitz continuity, Aleksandrov theorem and characterizations for \(H\)-convex functions

DOI10.1007/s00208-005-0717-4zbMath1115.49004OpenAlexW2021926521MaRDI QIDQ816962

Valentino Magnani

Publication date: 2 March 2006

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-005-0717-4

zbMATH Keywords

convex functionsstratified Lie groups

Mathematics Subject Classification ID

Convex functions and convex programs in convex geometry (52A41) Existence theories for problems in abstract spaces (49J27) Convexity of real functions in one variable, generalizations (26A51) Convexity of real functions of several variables, generalizations (26B25)

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Cites Work

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• Convex functions on Carnot groups
• Balls and metrics defined by vector fields. I: Basic properties
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Carathéodory spaces
• Weak differentiability of BV functions on stratified groups
• Convex functions on the Heisenberg group
• The theorem of Busemann-Feller-Alexandrov in Carnot groups
• On the second differentiability of convex surfaces
• Sub-Riemannian geometry. Proceedings of the satellite meeting of the first European congress of mathematics `Journées nonholonomes: géométrie sous-riemannienne, théorie du contrôle, robotique', Paris, France, June 30--July 1, 1992
• Notion of convexity in Carnot groups
• First-order regularity of convex functions on Carnot groups
• Viscosity convex functions on Carnot groups
• On second derivates of convex functions.
• ON ∞-HARMONIC FUNCTIONS ON THE HEISENBERG GROUP
• Differentiability from the representation formula and the Sobolev–Poincaré inequality
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• Surface measures in Carnot-Carathéodory spaces