测地线稳定性、射线空间与 Mabuchi 几何中的一致凸性
微分几何
2020-11-18 v4 复变函数
摘要
我们建立了关于常数量曲率 Kähler 度量存在性的 Donaldson 测地线稳定性猜想的本质最优形式。我们通过详细探究 Mabuchi 测地线射线的度量几何，以及 Kähler 度量空间的一致凸性性质来完成这一工作。
引用
@article{arxiv.1810.04661,
title = {Geodesic stability, the space of rays, and uniform convexity in Mabuchi geometry},
author = {Tamás Darvas and Chinh H. Lu},
journal= {arXiv preprint arXiv:1810.04661},
year = {2020}
}
备注
v2: Changes in presentation. References added. v3: We show that approximation is possible with C^11 rays with converging radial K-energy. As an application, we prove the C^11 uniform geodesic stability conjecture. v4: we shifted the main focus of the paper towards geodesic stability, reflected in the presentation and a new title