Sharp constants for Moser‐Trudinger inequalities on spheres in complex space ℂn

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Sharp Singular Trudinger–Moser Inequalities in Lorentz–Sobolev Spaces (2016, unknown): “, see [5, 13, 14, 22] and [16, 26, 27], respectively.”
Adams' inequalities for bi-Laplacian and extremal functions in dimension four (2009, unknown): “This idea has also been developed to derive the sharp constants for Adams’ inequality involving higher order derivatives on Riemannian manifolds without boundary by Fontana [17] and more recently in the subelliptic setting to derive the sharp Moser’s inequality on the Heisenberg group and CR sphere ”
Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications ✩ (2012, background): “The best constant for the sharp Moser–Trudinger inequality on CR sphere was also identified in [21].”
Sharp constant and extremal function for the improvedMoser-Trudinger inequality involving $L^p$ norm in two dimension (2009, methodology): “4) For the Moser-Trudinger inequalities and its extremal functions on Riemannian manifolds, we would like to mention the work by Fontana [9], Ding-Jost-Li-Wang [6], Druet-Hebey [7], and in the sub-Riemannian manifolds by Cohn-Lu [4, 5] and the references therein.”