Kähler-Einstein metrics and Ding functional on $\mathbb Q$-Fano group compactifications
Abstract
Let $G$ be a complex, connect reductive Lie group which is the complexification of a compact Lie group $K$. Let $M$ be a $\mathbb Q$-Fano $G$-compactification. In this paper, we first prove the uniqueness of $K\times K$-invariant (singular) Kähler-Einstein metric. Then we show the existence of (singular) Kähler-Einstein metric implies properness of the reduced Ding functional. Finally, we show that the barycenter condition is also necessary of properness.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2020
- DOI:
- 10.48550/arXiv.2008.13522
- arXiv:
- arXiv:2008.13522
- Bibcode:
- 2020arXiv200813522L
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematics - Functional Analysis;
- Primary: 53C25;
- Secondary: 32Q20;
- 58D25;
- 14L10