Existence problem of extremal Kaehler metrics

Toshiki Mabuchi

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arXiv · 1307.5203

Existence problem of extremal Kaehler metrics

Toshiki Mabuchi

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Abstract

In this paper, we shall give some affirmative answer to an extremal Kaehler version of the Yau-Tian-Donaldson Conjecture. For a polarized algebraic manifold $(X,L)$, we choose a maximal algebraic torus $T$ in the group of holomorphic automorphisms of $X$. Then the polarization class $c_1(L)$ will be shown to admit an extremal Kaehler metric if $(X,L)$ is strongly K-stable relative to $T$.

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Toshiki Mabuchi. 2013-07-19. Existence problem of extremal Kaehler metrics. https://arxiv.org/abs/1307.5203

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