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Extremals for the Sobolev inequality on the seven-dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem

Stefan Ivanov, Ivan Minchev, Dimiter Vassilev (2010)

Journal of the European Mathematical Society

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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