Approximation of weak geodesics and subharmonicity of Mabuchi energy, II: $\epsilon$-geodesics
Differential Geometry
2022-08-30 v2
Abstract
The purpose of this article is to study the strict convexity of the Mabuchi functional along a -geodesic, with the aid of the -geodesics. We proved the -convergence of the fiberwise volume element of the -geodesic. Moreover, the geodesic is proved to be uniformly fiberwise non-degenerate if the Mabuchi functional is -affine.
Keywords
Cite
@article{arxiv.2102.05277,
title = {Approximation of weak geodesics and subharmonicity of Mabuchi energy, II: $\epsilon$-geodesics},
author = {Long Li},
journal= {arXiv preprint arXiv:2102.05277},
year = {2022}
}
Comments
We corrected some errors and typos, and added several remarks and more details to explain this paper. Moreover, the more complicated proof of the strong L^2-convergence of the fiberwise volume element of the epsilon geodesic has been moved to the Appendix, and only remain the simpler one in the main context