The Calabi functional on a ruled surface

Abstract

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

23 pages, 3 figures

References in corpus (1)

• Hamiltonian 2-forms in Kahler geometry, III Extremal metrics and stability

Cited by in corpus (4)

• Lectures on Stability and Constant Scalar Curvature
• The Calabi flow on Kähler surface with bounded Sobolev constant
• On the Extension of the Calabi Flow on Toric Varieties
• Local solution and extension to the Calabi flow