Singular Liouville Equations on $S^2$ : Sharp Inequalities and Existence Results

preprint2015arXivOpen access

We prove a sharp Onofri-type inequality and non-existence of extremals for a Moser-Tudinger functional on the sphere in the presence of potentials having positive order singularities. We also investigate the existence of critical points and give some sufficient conditions under symmetry or nondegeneracy assumptions.

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Singular Liouville Equations on $S^2$ : Sharp Inequalities and Existence Results

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Singular Liouville Equations on S2S^2S2: Sharp Inequalities and Existence Results

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Singular Liouville Equations on $S^2$ : Sharp Inequalities and Existence Results