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arXiv · 1310.5827

Removable sets for Lipschitz harmonic functions on Carnot groups

Vasilis Chousionis·Valentino Magnani·Jeremy T. Tyson
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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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Vasilis Chousionis, Valentino Magnani, Jeremy T. Tyson. 2013-10-22. Removable sets for Lipschitz harmonic functions on Carnot groups. https://arxiv.org/abs/1310.5827

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