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

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

2007-03-01

arxiv.org/abs/math/0703044v3

Mathematics

Differential Geometry

22 pages, LaTeX 2e, 10pt, exposition extended and clarified, typos corrected, final version to appear in the Journal of the Eu

Scientific paper

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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