Capacities Characterizing Removable Sets for Various Function Spaces in Carnot Groups

2025/12/19 by Zack Boone, Boone, Zack
Engineering · Mathematics · #Carnot cycle #Classical Analysis and ODEs (math.CA) #Differential (mechanical device) #FOS: Mathematics #Function (biology) #Geometric Analysis and Curvature Flows #Homogeneity (statistics) #Hypoelliptic operator #Linear map #Lipschitz continuity #Nonlinear Partial Differential Equations #Operator (biology) #Stability and Controllability of Differential Equations

paper · open access · doi:10.48550/arxiv.2512.17167

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/12/19 · openalex created_date 2025/12/23 · openalex updated_date 2026/07/28

Abstract

We study removable sets for the Campanato, Hölder continuous, L^p_loc, and Lipschitz functions in Carnot groups. In the former three cases, we characterize removability through the use of capacities with respect to any left-invariant linear differential operator L for which L and L^t are hypoelliptic and satisfy a homogeneity condition, while in the latter case we characterize Lipschitz functions with respect to the sub-Laplacian.

Citations

• A new differentiation, shape of the unit ball and perimeter measure
• Removable sets for Lipschitz harmonic functions on Carnot groups
• Painleve's problem and the semiadditivity of analytic capacity
• Metriques de Carnot-Caratheodory et Quasiisometries des Espaces Symetriques de rang un

Related

• Removable sets for Lipschitz harmonic functions on Carnot groups
• Lipschitz and biLipschitz Maps on Carnot Groups
• Intrinsically Lipschitz functions with normal target in Carnot groups
• Carnot rectifiability and Alberti representations
• Coarse differentiation and quantitative nonembeddability for Carnot groups