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.