On the space of Kahler potentials

Weiyong He

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arXiv · 1208.1021

On the space of Kahler potentials

Weiyong He

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Abstract

We consider the geodesic equation for the generalized Kahler potential with only mixed second derivatives bounded. We show that given such two generalized Kahler potentials, there is a unique geodesic segment such that for each point on the geodesic, the generalized Kahler potential has uniformly bounded mixed second derivatives (in manifold directions). This generalizes a fundamental theorem of Chen \cite{Chen00} on the space of Kahler potentials.

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Weiyong He. 2012-08-05. On the space of Kahler potentials. https://arxiv.org/abs/1208.1021

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