A complete solution to the quaternionic contact Yamabe problem on the seven dimensional sphere is given. Extremals for the Sobolev inequality on the seven dimensional Heisenberg group are explicitly described and the best constant in the L2 Folland–Stein embedding theorem is determined.
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Ivan Minchev, Stefan Ivanov, Dimiter Vassilev, Extremals for the Sobolev inequality on the seven-dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem. J. Eur. Math. Soc. 12 (2010), no. 4, pp. 1041–1067DOI 10.4171/JEMS/222