Removable sets for Lipschitz harmonic functions on Carnot groups

Published 22 Oct 2013 in math.AP | (1310.5827v1)

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.

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