Universal differentiability sets in Carnot groups of arbitrarily high step

DOI10.1007/s11856-020-2069-xzbMath1475.53036arXiv1711.11433OpenAlexW3088160493MaRDI QIDQ2218723

Gareth Speight, Andrea Pinamonti

Publication date: 18 January 2021

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.11433

zbMATH Keywords

Carnot groupPansu differentiabilityfiliform groupsuniversal differentiability setRademacher

Mathematics Subject Classification ID

Nilpotent and solvable Lie groups (22E25) Sub-Riemannian geometry (53C17)

Related Items (3)

Rigidity results in diffusion Markov triples ⋮ A \(C^{m,\omega}\) Whitney extension theorem for horizontal curves in the Heisenberg group ⋮ A \(C^m\) Lusin approximation theorem for horizontal curves in the Heisenberg group

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the differentiability of Lipschitz functions with respect to measures in the Euclidean space
• Differentiability inside sets with Minkowski dimension one
• Sard property for the endpoint map on some Carnot groups
• A compact universal differentiability set with Hausdorff dimension one
• A universal differentiability set in Banach spaces with separable dual
• A compact null set containing a differentiability point of every Lipschitz function
• An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
• Differentiability of Lipschitz functions on Banach spaces
• A sufficient condition for nonrigidity of Carnot groups
• Balls and metrics defined by vector fields. I: Basic properties
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• Differentiability of Lipschitz functions on metric measure spaces
• Universal differentiability sets and maximal directional derivatives in Carnot groups
• Porosity and differentiability of Lipschitz maps from stratified groups to Banach homogeneous groups
• Differentiability of Lipschitz functions in Lebesgue null sets
• Cone unrectifiable sets and non-differentiability of Lipschitz functions
• Quasi-conformal maps on model filiform groups
• A measure zero universal differentiability set in the Heisenberg group
• Intrinsic Lipschitz graphs within Carnot groups
• Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung
• TOWARDS DIFFERENTIAL CALCULUS IN STRATIFIED GROUPS
• Radon–Nikodym Property and Area Formula for Banach Homogeneous Group Targets
• Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians
• Differentiation of Real-Valued Functions and Continuity of Metric Projections
• Contact and quasiconformal mappings on real model filiform groups
• A Comprehensive Introduction to Sub-Riemannian Geometry
• On the codimension of the abnormal set in step two Carnot groups

This page was built for publication: Universal differentiability sets in Carnot groups of arbitrarily high step