On the space of Kahler potentials

2012/08/05 by Weiyong He, He, Weiyong
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1208.1021

openalex publication_date 2012/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citeChen00 on the space of Kahler potentials.

Citations

• The Space of Kähler metrics (II)

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