||Uniqueness results on CR manifolds
||Ho, Pak Tung
||ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2021
||In this paper we show the uniqueness of the constant solution to a general Yamabe-type equation on a compact pseudohermitian manifold. The Riemannian version was first proved by Bidaut-Veron and Veron. In another direction, we make use of the vanishing property of two eigenfunctions of the sub-Laplacian to conclude the nonvanishing of the first cohomology group of a compact pseudohermitian manifold. The corresponding version for the Riemannian case was first proved by Gichev.