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Two variational problems in Kähler geometry
Published 1 May 2024 in math.CV, math.DG, and math.MG | (2405.00869v1)
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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