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The Calabi functional on a ruled surface

Gábor Székelyhidi
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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.

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Gábor Székelyhidi. 2007-03-19. The Calabi functional on a ruled surface. https://arxiv.org/abs/math/0703562

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