Wermer examples and currents

Details Wermer examples and currents Wermer examples and currents

2009-04-27

arxiv.org/abs/0904.4179v3

Mathematics

Complex Variables

Minor modifications. Final version, to appear in GAFA

Scientific paper

In this paper we give the first examples of positive closed currents in $\mathbb{C}^2$ with continuous potentials, vanishing self-intersection, and which are not laminar. More precisely, they are supported on sets "without analytic structure". The result is mostly interesting when the potential has regularity close to $C^2$, because laminarity is expected to hold in that case. We actually construct examples which are $C^{1,\alpha}$ for all $\alpha<1$.

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