A Harnack type inequality for the Yamabe equation in low dimensions

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A compactness theorem for a fully nonlinear Yamabe problem under a lower Ricci curvature bound (2012, background): “For n = 3, 4, 5, see works of Li and Zhu [34], Druet [14, 15] and Li and Zhang [31].”
Compactness of solutions to the Yamabe problem (2004, methodology): “For general manifolds of dimension n = 3, a proof was given by Li and Zhu in [73]; while for n = 4, a combination of the results of Li and Zhang [ 70 ] and Druet [44] yields a proof, with the H1 bound given in [70] and the L∞ bound under the assumption of an H1”