K-energy on polarized compactifications of Lie groups

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.

40pages, 4 figures

References in corpus (2)

• 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

Cited by in corpus (2)

• Mabuchi metrics and properness of the modified DING functional
• $G$-Sasaki manifolds and K-energy