Removable sets for Lipschitz harmonic functions on Carnot groups
Analysis of PDEs
2013-10-23 v1
Abstract
Let G be a Carnot group with homogeneous dimension Q larger than 2 and let L be a sub-Laplacian on G. We prove that the critical dimension for removable sets of Lipschitz L-harmonic functions is Q-1. Moreover we construct self-similar sets with positive and finite (Q-1) dimensional Hausdorff measure which are removable.
Cite
@article{arxiv.1310.5827,
title = {Removable sets for Lipschitz harmonic functions on Carnot groups},
author = {Vasilis Chousionis and Valentino Magnani and Jeremy T. Tyson},
journal= {arXiv preprint arXiv:1310.5827},
year = {2013}
}
Comments
24 pages