Strict convexity of the Mabuchi functional for energy minimizers

2017/11/27 by Long Li, Li, Long
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #math.DG

paper · pdf · doi:10.48550/arxiv.1711.09717

arxiv created 2017/11/27 · arxiv updated 2017/11/28

Abstract

There are two parts of this paper. First, we discovered an explicit formula for the complex Hessian of the weighted log-Bergman kernel on a parallelogram domain, and utilised this formula to give a new proof about the strict convexity of the Mabuchi functional along a smooth geodesic. Second, when a C^1,1-geodesic connects two non-degenerate energy minimizers, we also proved this strict convexity, by showing that such a geodesic must be non-degenerate and smooth.

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