Gauld, D. B.; Martin, G. J. Essential singularities of quasimeromorphic mappings. (English) Zbl 0792.30015 Math. Scand. 73, No. 1, 36-40 (1993). Suppose that \(f:\mathbb{B}^ n-\{0\} \to S^ n\) is a quasi-meromorphic mapping, where \(B^ n\) is the open unit ball in euclidean \(n\)-space and \(S^ n\) the unit sphere in euclidean \((n+1)\)-space. If 0 is an essential singularity then in every deleted neighbourhood of 0 there is an essential round sphere on which \(f\) assumes antipodal values. Thus if \[ \limsup_{| x |=| y |=r \to 0} q(f(x),f(y))<1, \] where \(q\) is the chordal metric normalised so that \(q(S^ n)=1\), then 0 is a removable singularity for \(f\). Reviewer: D.B.Gauld Cited in 1 Document MSC: 30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations Keywords:quasi-meromorphic mapping; essential singularity; removable singularity PDFBibTeX XMLCite \textit{D. B. Gauld} and \textit{G. J. Martin}, Math. Scand. 73, No. 1, 36--40 (1993; Zbl 0792.30015) Full Text: DOI EuDML