弱测地线的逼近与 Mabuchi 能量的次调和性，II：$\epsilon$-测地线
微分几何
2022-08-30 v2
摘要
本文旨在借助 -测地线研究 Mabuchi 泛函沿 -测地线的严格凸性。我们证明了 -测地线的纤维体积元的 -收敛性。此外，若 Mabuchi 泛函是 -仿射的，则证明该测地线是一致纤维wise非退化的。
引用
@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}
}
备注
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