常数$μ$ -数量曲率Kähler度量--公式和基本结果
Constant $μ$-scalar curvature Kähler metric -- formulation and foundational results
摘要：
引入了具有矩映射μ的K“ahler度量的μ-数量曲率，并研究了常数μ-数量曲率K“ahler度量，作为cscK度量和K“ahler-Ricci孤子的推广，作为通向极值度量的一条连续路径.通过研究一个与Perelman的W-泛函密切相关的体积泛函，我们研究了常数μ-数量曲率K“ahler度量存在的一些基本约束.研究了一种新的K-能量，作为解决常数μ-数量曲率唯一性问题的一种方法，并作为新的K-稳定性概念的前奏.
英文摘要：
We introduce mu-scalar curvature for a K"ahler metric with a moment map mu and start up a study on constant mu-scalar curvature K"ahler metric as a generalization of both cscK metric and K"ahler-Ricci soliton and as a continuity path to extremal metric. We study some fundamental constraints to the existence of constant mu-scalar curvature K"ahler metric by investigating a volume functional as a generalization of Tian-Zhu's work, which is closely related to Perelman's W-functional. A new K-energy is studied as an approach to the uniqueness problem of constant mu-scalar curvature and as a prelude to new K-stability concept.
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