The Calabi functional on a ruled surface

Székelyhidi, Gábor

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 42 (2009) no. 5, pp. 837-856.

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.

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.

Classification : 53C55, 53C44
Keywords: Calabi functional, Calabi flow
Mot clés : fonctionnelle de Calabi, flot de Calabi

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