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arXiv · 2405.00869

Two variational problems in K\"ahler geometry

Laszlo Lempert
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Abstract

On a K\"ahler manifold we consider the problems of maximizing/minimizing Monge--Amp\`ere energy over certain subsets of the space of K\"ahler potentials. Under suitable assumptions we prove that solutions to these variational problems exist, are unique, and have a simple characterization. We then use the extremals to construct hermitian metrics on holomorphic vector bundles, and investigate their curvature.

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Laszlo Lempert. 2024-05-01. Two variational problems in K\"ahler geometry. https://arxiv.org/abs/2405.00869

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