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Uniqueness of solutions to singular Liouville-type equations

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No logo availableBanff International Research Station (BIRS) for Mathematical Innovation and Discovery
 Jevnikar, Aleks

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Uniqueness of solutions to singular Liouville-type equations
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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We deduce new uniqueness results for solutions to singular Liouville-type equations both on spheres and on bounded domains, as well as new self-contained proofs of previously known results. To this end, we derive a singular Sphere Covering Inequality based on the singular Alexandrov-Bol isoperimetric inequality and symmetric rearrangements.