On isoperimetric inequality in Arakelov geometry

Chen, Huayi

Bulletin de la Société Mathématique de France, Tome 146 (2018) no. 4, pp. 649-673

We establish an isoperimetric inequality in an integral form and deduce a relative version of Brunn-Minkowski inequality in the Arakelov geometry setting.

On établit une inégalité isopérimétrique sous une forme d’intégration dans le cadre de géométrie d’Arakelov et en déduit une version relative de l’inégalité de Brunn-Minkowski dans le même cadre.

Classification : 14G40, 11G30
Keywords: Arakelov geometry, isoperimetric inequality, Brunn-Minkowski inequality
Mots-clés : Géométrie d’Arakelov, inégalité isopérimétrique, inégalité de Brunn-Minkowski

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