Kähler Metric with Constant Weighted Scalar Curvature and Weighted K-stability
发布时间：2018年10月01日
浏览次数：5600
发布者: He Liu
主讲人： Abdellah Lahdili (Université du Québec à Montréal)
活动时间： 从 2018-10-10 15:00 到 17:00
场地： 北京国际数学研究中心，全斋全29教室
We introduce a notion of a Kähler metric with constant weighted scalar curvature on a compact Kähler manifold X, depending on a fixed real torus T in the reduced group of automorphisms of X, and two smooth (weight) functions, defined on the momentum image (with respect to a given Kähler class on X) of X in the dual Lie algebra of T. A number of natural problems in Kähler geometry, such as the existence of extremal Kähler metrics and conformally Kähler, Einstein{Maxwell metrics, or Kähler-Ricci solitons reduce to the search of Kähler metrics with constant weighted scalar curvature in a given Kähler class, for special choices of the weight functions.
We define a notion of weighted Mabuchi energy adapted to our setting, and of a weighted Futaki invariant of a T-compatible smooth Kähler test configuration associated to (X; T), and show that the boundedness from below of the weighted Mabuchi energy implies a suitable notion of a weighted K-semistability.
We define a notion of weighted Mabuchi energy adapted to our setting, and of a weighted Futaki invariant of a T-compatible smooth Kähler test configuration associated to (X; T), and show that the boundedness from below of the weighted Mabuchi energy implies a suitable notion of a weighted K-semistability.
