Mabuchi's soliton metric and relative D-stability

Abstract

For Fano manifolds T. Mabuchi introduced a generalization of the K\"ahler-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. The idea of the proof includes some equivariant generalization of the recent developed variational approach to the K\"ahler-Einstein problem.

Locations

• American Journal of Mathematics - View
• arXiv (Cornell University) - View - PDF