## Structure of compacta generating normal domains and removal singularities for the space $$L^ 1_ p(D)$$.(Russian)Zbl 0716.30013

The author examines the properties of p-normal regions in $${\mathbb{R}}^ n$$, $$1<p<+\infty$$, which, with $$n=p=2$$, are minimal in the sense of Koebe or normal in the sense of Grötsch. He gives a description of removable singularities for the space $$L^ 1_ p(D)$$ and of compacta generating p-normal regions, in terms of contingency theory and the (n-1)- dimensional bilipschitzian $$NC_ p$$-compacta. Apart from interesting new results, the paper includes generalizations of many well-known results from the geometry of $$NC_ p$$-sets and $$N_ p$$-compacta.
Reviewer: L.Mikołajczyk

### MSC:

 30C65 Quasiconformal mappings in $$\mathbb{R}^n$$, other generalizations 30C85 Capacity and harmonic measure in the complex plane
Full Text: