Wermer examples and currents

Abstract

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 $\alpha <1$.

Minor modifications. Final version, to appear in GAFA