Approximation of weak geodesics and subharmonicity of Mabuchi energy, II: ε-geodesics

2021/02/10 by Long Li, Li, Long
Mathematics · Physics and Astronomy · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.2102.05277

Abstract

The purpose of this article is to study the strict convexity of the Mabuchi functional along a C^1,1-geodesic, with the aid of the ε-geodesics. We proved the L²-convergence of the fiberwise volume element of the ε-geodesic. Moreover, the geodesic is proved to be uniformly fiberwise non-degenerate if the Mabuchi functional is ε-affine.

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