JournalsjemsVol. 12 , No. 4DOI 10.4171/jems/222

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

  • Ivan Minchev

    University of Sofia, Bulgaria
  • Stefan Ivanov

    University of Sofia, Bulgaria
  • Dimiter Vassilev

    University of New Mexico, Albuquerque, United States
Extremals for the Sobolev inequality on the seven-dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem cover

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.