Mabuchi's soliton metric and relative D-stability

Abstract

For Fano manifolds T. Mabuchi introduced a generalization of the Kähler-Einstein metric, which is characterized as the critical point of the Ricci-Calabi functional. We show that a Fano manifold admits Mabuchi's metric if and only if it is uniformly relatively D-stable.

We fixed the proof of the main theorem in the first version, following the work of Professor C. Li