The CR Yamabe conjecture the case n = 1

By Najoua Gamara. 2001

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A Positive Mass Theorem in Three Dimensional Cauchy–Riemann Geometry (2013, methodology): “oposition 4.4 there might be examples of pseudohermitian manifolds of positive Tanaka-Webster class for which there is no minimizer. In this case, the use of variational or topological methods (as in [23], [24]) seems to be a necessary tool in order to ﬁnd conformal structures of constant Tanaka-Web”
EXISTENCE OF SOLUTIONS AND REGULARITY NEAR THE CHARACTERISTIC BOUNDARY FOR SUB-LAPLACIAN EQUATIONS ON CARNOT GROUPS (2006, methodology): “The solution of this problem is instrumental for solving the general case, which is complete after the works of Jerison and Lee [1984; 1987; 1988; 1989], and Gamara and Yacoub [Gamara 2001; Gamara and Yacoub 2001].”
A perturbation result for the Webster scalar curvature problem on the CR sphere (2002, background): “Indeed, in the papers [27–29], Jerison and Lee extensively studied the Yamabe problem on CR manifolds (see also the recent papers by Gamara and Yacoub [22,23] which treat the cases left open by Jerison and Lee).”
CR Yamabe conjecture – the conformally flat case (2001, background): “In [ 9 ], the case n=1, but without anyhypothesis of CR conformal flatness is studied.”