Extremals for the Sobolev inequality on the seven dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem
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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 Hesenberg group are explicitly described and the best constant in the $L^2$ Folland-Stein embedding theorem is determined.
22 pages, LaTeX 2e, 10pt, exposition extended and clarified, typos corrected, final version to appear in the Journal of the European Math. Soc. (JEMS)
22 pages, LaTeX 2e, 10pt, exposition extended and clarified, typos corrected, final version to appear in the Journal of the European Math. Soc. (JEMS)