K-energy on polarized compactifications of Lie groups
arXiv:1701.00306
Abstract
In this paper, we study Mabuchi's K-energy on a compactification M of a reductive Lie group G, which is a complexification of its maximal compact subgroup K. We give a criterion for the properness of K-energy on the space of K \times K-invariant Kahler potentials. In particular, it turns to give an alternative proof of Delcroix's theorem for the existence of Kahler-Einstein metrics in case of Fano manifolds M . We also study the existence of minimizers of K-energy for general Kahler classes of M.
arXiv comment40pages, 4 figures
References in corpus (5)
- Tian's properness conjectures and Finsler geometry of the space of Kahler metrics
- K-Stability of Fano spherical varieties
- Kähler-Einstein metrics on group compactifications
- Convexity of the K-energy on the space of Kahler metrics and uniqueness of extremal metrics
- The Weyl Integration Model for KAK decomposition of Reductive Lie Group