The role of Onofri type inequalities in the symmetry properties of extremals for Caffarelli-Kohn-Nirenberg inequalities, in two space dimensions

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An Improved Geometric Inequality via Vanishing Moments, with Applications to Singular Liouville Equations (2012, background): “Notice that this condition relaxes the radiality in [36] to a two-dimensional constraint, and that it allows an arbitrarily small scale of concentration at a single point (so [21] would not apply).”