Ein neues Schlitztheorem der konformen Abbildung.
The original version of the article was published in Central European Journal of Mathematics, 2005, 3(4), 591–605. Unfortunately, the original version of this article contains a mistake. We give some corrections to our work.
We establish inequalities for Green functions on general bounded piecewise Dini-smooth Jordan domains in ℝ². This enables us to prove a new version of the 3G Theorem which generalizes its previous version given in [M. Selmi, Potential Anal. 13 (2000)]. Using these results, we give a comparison theorem for the Green kernel of Δ and the Green kernel of Δ - μ, where μ is a nonnegative and exact Radon measure.