The Calabi functional on a ruled surface

[La fonctionnelle de Calabi sur une surface réglée]

Székelyhidi, Gábor

Annales scientifiques de l'École Normale Supérieure, Tome 42 (2009), p. 837-856 / Harvested from Numdam

Résumé

On étudie la fonctionnelle de Calabi sur une surface réglée au-dessus d'une courbe de genre deux. Pour les polarizations qui n'admettent pas de métrique extrémale, on décrit le comportement d'une suite minimisante partitionnant la variété. On montre aussi que le flot de Calabi partant d'une métrique avec une symétrie appropriée produit une telle suite minimisante.

Abstract

We study the Calabi functional on a ruled surface over a genus two curve. For polarizations which do not admit an extremal metric we describe the behavior of a minimizing sequence splitting the manifold into pieces. We also show that the Calabi flow starting from a metric with suitable symmetry gives such a minimizing sequence.

Détail

Publié le : 2009-01-01

MR 2571959 | Zbl 1187.58020

DOI : https://doi.org/10.24033/asens.2110
Classification:  53C55,  53C44
Mots clés: fonctionnelle de Calabi, flot de Calabi

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