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arXiv · 1609.01512

On a singular Liouville-type equation and the Alexandrov isoperimetric inequality

Daniele Bartolucci·Daniele Castorina
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Abstract

We obtain a generalized version of an inequality, first derived by C. Bandle in the analytic setting, for weak subsolutions of a singular Liouville-type equation. As an application we obtain a new proof of the Alexandrov isoperimetric inequality on singular abstract surfaces. Interestingly enough, motivated by this geometric problem, we obtain a seemingly new characterization of local metrics on Alexandrov's surfaces of bounded curvature. At least to our knowledge, the characterization of the equality case in the isoperimetric inequality in such a weak framework is new as well.

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Daniele Bartolucci, Daniele Castorina. 2016-09-06. On a singular Liouville-type equation and the Alexandrov isoperimetric inequality. https://doi.org/10.2422/2036-2145.201609_001

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