论文标题
力矩图，凸功能和极端点
Moment map, convex function and extremal point
论文作者
论文摘要
MONG MAP $μ$是研究符号歧管上紧凑型谎言组$ k $的研究的中心概念。简而言之，我们提出了一个力矩理论，并与$ \ mathfrak上的$ \ mathrm {ad} _k $ -invariant convex函数$ f $ function in $ \ mathfrak {k}^{\ ast} $，$ k $的lie algebra of $ k $的属性，并研究$ f \ f \ cound的属性。我们的动机来自Donaldson \ Cite {Donaldson2017}，这是我们设置的无限尺寸版本的一个例子。作为应用程序，我们将Kähler-Icci solitons解释为广义极端指标的特殊情况。
The moment map $μ$ is a central concept in the study of Hamiltonian actions of compact Lie groups $K$ on symplectic manifolds. In this short note, we propose a theory of moment maps coupled with an $\mathrm{Ad}_K$-invariant convex function $f$ on $\mathfrak{k}^{\ast}$, the dual of Lie algebra of $K$, and study the properties of the critical point of $f\circμ$. Our motivation comes from Donaldson \cite{Donaldson2017} which is an example of infinite dimensional version of our setting. As an application, we interpret Kähler-Ricci solitons as a special case of the generalized extremal metric.
