Two variational problems in Kähler geometry

2024/05/01 by Lempert, Laszlo · 2 citations
#32Q15 #32U05 #32W20 #52A40 #58E40 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2405.00869

Abstract

On a Kähler manifold we consider the problems of maximizing/minimizing Monge--Ampère energy over certain subsets of the space of Kähler 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.

Cited by

• Uniform RC-positivity of direct image bundles
• Mean curvature of direct image bundles

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