, Volume 21, Issue 5, pp 1196-1217

New Improved Moser–Trudinger Inequalities and Singular Liouville Equations on Compact Surfaces

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We consider a singular Liouville equation on a compact surface, arising from the study of Chern–Simons vortices in a self-dual regime. Using new improved versions of the Moser–Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.