We prove that the critical dimension for removable sets of Lipschitz L-harmonic functions is Q-1, where Q is the Hausdorff dimension of the Carnot group, the sub-Laplacian L is defined and Q is not less than 3. Moreover, we construct self-similar sets with positive and finite Hausdorff measure of dimension Q-1, which are removable.
Removable sets for Lipschitz harmonic functions on Carnot groups
MAGNANI, VALENTINO;
2015-01-01
Abstract
We prove that the critical dimension for removable sets of Lipschitz L-harmonic functions is Q-1, where Q is the Hausdorff dimension of the Carnot group, the sub-Laplacian L is defined and Q is not less than 3. Moreover, we construct self-similar sets with positive and finite Hausdorff measure of dimension Q-1, which are removable.File in questo prodotto:
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