Harmonic forms and Riesz transforms for rank one symmetric spaces

Abstract

We study harmonic forms on a noncompact rank one symmetric space M\ that is, differential forms satisfying the equations dco = 0, ôco = 0. We define "Hardy spaces" H p of harmonic forms on M and study their bound-

The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds

“…We remark that (3.7) is a solution to the Yamabe equation on any group of Heisenberg type [101] which was found earlier (and seems to have been forgotten) in the case of Iwasawa groups in [144,Proposition2]. It also should be noted that [140] and [122] actually determine all critical points of the associated to (3.1) variational problem rather than only the functions with lowest energy.…”