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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
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Abstract

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.

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Stefan Ivanov, Ivan Minchev, Dimiter Vassilev. 2008-07-30. Extremals for the Sobolev inequality on the seven dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem. https://arxiv.org/abs/math/0703044

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