论文标题
加权mabuchi功能和加权极好指标的独特性的凸度
Convexity of the weighted Mabuchi functional and the uniqueness of weighted extremal metrics
论文作者
论文摘要
我们证明了一个合适的复杂自动形态亚组的元素的唯一性，直到背带，在我们以前的工作中引入的紧凑型Kähler歧管上，加权的极值Kähler指标。这扩展了极端Kähler案中Berman-Berndtsson和Chen-Paun-Zeng的结果。此外，我们表明，加权的极值kähler指标是改良mabuchi能量的合适加权版本的全球最低限度。这意味着Kähler歧管承认加权的极值Kähler指标的合适的加权K-敏感性概念。
We prove the uniqueness, up to a pull-back by an element of a suitable subgroup of complex automorphisms, of the weighted extremal Kähler metrics on a compact Kähler manifold introduced in our previous work. This extends a result by Berman--Berndtsson and Chen--Paun--Zeng in the extremal Kähler case. Furthermore, we show that a weighted extremal Kähler metric is a global minimum of a suitable weighted version of the modified Mabuchi energy. This implies a suitable notion of weighted K-semistability of a Kähler manifold admitting a weighted extremal Kähler metric.
