Strict convexity of the Mabuchi functional for energy minimizers
Differential Geometry
2017-11-28 v1 Complex Variables
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.
Keywords
Cite
@article{arxiv.1711.09717,
title = {Strict convexity of the Mabuchi functional for energy minimizers},
author = {Long Li},
journal= {arXiv preprint arXiv:1711.09717},
year = {2017}
}