Singular Liouville Equations on S²: Sharp Inequalities and Existence Results
classification
🧮 math.AP
math.DG
keywords
existencesharpassumptionsconditionscriticalequationsextremalsfunctional
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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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