Removable sets for Lipschitz harmonic functions on Carnot groups

Chousionis Vasilis - Magnani Valentino - Tyson Jeremy T.

year: 2013
abstract: Let $\mathbb G$ be a Carnot group with homogeneous dimension $Q \geq 3$ and let $\mathcal L$ be a sub-Laplacian on $\mathbb G$. We prove that the critical dimension for removable sets of Lipschitz $\mathcal L$-harmonic functions is $(Q-1)$. Moreover we construct self-similar sets with positive and finite ${\mathcal H}^{Q-1}$ measure which are removable.

The paper is available on the cvgmt preprint server.