Communications in Analysis and Geometry
Volume 12 (2004)
K Energy and K Stability on Hypersurfaces
Pages: 601 – 630
Suppose that M is a compact Fano manifold. That is, M is a compact Kähler manifold with positive first Chern class. One of the most important problems in Kähler geometry is the existence of Kähler metrics of constant scalar curvature. It is believed that the problem is related to certain notion of stability in the sense of Geometric Invariant Theory.
In Tian  and Donaldson , the notion of K stability was introduced. In the first three sections of this paper, we use the notations in  to derive our theorems. In the last section, we discuss the definition of  and some observations motivated by that paper.