Classification of finite energy positive solutions to Yamabe-type equation on the fifteen dimensional octonionic Heisenberg group

We classify finite-energy positive solutions to the Yamabe-type equation on the 15-dimensional octonionic Heisenberg group, whose algebra is non-associative. Extremals for the Folland-Stein-Sobolev inequality on this group are explicitly described. This confirms the conjecture of Garofalo and Vassilev [Duke Math. J. 2001] on the $15$ dimensional octonionic Heisenberg group.