On a singular Liouville-type equation and the Alexandrov isoperimetric inequlity
| Autor: | Daniele Bartolucci, Daniele Castorina |
|---|---|
| Přispěvatelé: | Bartolucci, D, Castorina, D |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Surfaces of Bounded Curvature 35B45 35J75 35R05 35R45 30F45 53B20 Alexandrov’s Isoperimetric inequality Theoretical Computer Science Type equation Mathematics - Analysis of PDEs Mathematics (miscellaneous) Settore MAT/05 - Analisi Matematica FOS: Mathematics Singular Liouville-type equations Mathematics::Metric Geometry Mathematics::Differential Geometry Isoperimetric inequality Singular Liouville-type equations Alexandrov’s Isoperimetric inequality Surfaces of Bounded Curvature Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE. :35-64 |
| ISSN: | 2036-2145 0391-173X |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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