Eastwood, Michael Uniqueness of the stereographic embedding. (English) Zbl 1340.53012 Arch. Math., Brno 50, No. 5, 265-271 (2014). The author studies the question of the conformal compactification of \(\mathbb{R}^n\), \(n \geq 3\). It is not suprising that the only such compactification is \(S^n\) with the round metric. It was proved in [C. Frances, “Rigidity at the boundary for conformal structures and other Cartan geometries”, Preprint, arxiv:0806.1008]. The author’s aim is to provide a much more elementary proof based on so-called conformal geodesics. Their characterization is well known but significantly more complicated than for Riemannian geodesics. After a nice summary of properties of conformal geodesics, and using the notion of so-called highly accessible points at the boundary, author provides a very elementary (and elegant) proof. Reviewer: Martin Čadek (Brno) Cited in 2 Documents MSC: 53A30 Conformal differential geometry (MSC2010) 53C22 Geodesics in global differential geometry Keywords:stereographic projection; conformal circles; compactification PDFBibTeX XMLCite \textit{M. Eastwood}, Arch. Math., Brno 50, No. 5, 265--271 (2014; Zbl 1340.53012) Full Text: DOI arXiv