Calculus of Variations and Geometric Measure Theory
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D. Bartolucci - D. Castorina

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

created by castorina on 25 Jul 2017
modified on 31 Oct 2018


Accepted Paper

Inserted: 25 jul 2017
Last Updated: 31 oct 2018

Journal: Annali della Scuola Normale Superiore di Pisa-Classe di Scienze
Year: 2017

ArXiv: 1609.01512v1 PDF


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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