Uniqueness of the stereographic embedding

Michael Eastwood

Address: Mathematical Sciences Institute, Australian National University, ACT 0200, Australia

E-mail: meastwoo@member.ams.org

Abstract: The standard conformal compactification of Euclidean space is the round sphere. We use conformal geodesics to give an elementary proof that this is the only possible conformal compactification.

AMSclassification: primary 53A30; secondary 53C22.

Keywords: stereographic, conformal circles, compactification.

DOI: 10.5817/AM2014-5-265