Extremals for the Sobolev inequality on the seven-dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem
Stefan Ivanov
University of Sofia, BulgariaIvan Minchev
University of Sofia, BulgariaDimiter Vassilev
University of New Mexico, Albuquerque, United States
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 Heisenberg group are explicitly described and the best constant in the L2 Folland–Stein embedding theorem is determined.
Cite this article
Stefan Ivanov, Ivan Minchev, Dimiter Vassilev, Extremals for the Sobolev inequality on the seven-dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem. J. Eur. Math. Soc. 12 (2010), no. 4, pp. 1041–1067
DOI 10.4171/JEMS/222