Kähler–Einstein Metrics and Ding Functional on ℚ-Fano Group Compactifications

Yan Li; Zhenye Li

doi:10.1007/s10114-025-2511-4

Kähler–Einstein Metrics and Ding Functional on ℚ-Fano Group Compactifications

Yan Li
, Zhenye Li^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Let G be a complex, connected reductive Lie group which is the complexification of a compact Lie group K. Let M be a ℚ-Fano G-compactification. In this paper, we first prove a uniqueness result of K × K-invariant (singular) Kähler–Einstein metrics on M. Then we show the existence of (singular) Kähler–Einstein metric implies properness of the reduced Ding functional. This gives a refinement of the properness conjecture on group compactifications.

Original language	English
Pages (from-to)	2555-2572
Number of pages	18
Journal	Acta Mathematica Sinica, English Series
Volume	41
Issue number	10
DOIs	https://doi.org/10.1007/s10114-025-2511-4
Publication status	Published - Oct 2025
Externally published	Yes

Keywords

14L10
32Q20
53C25
58D25
Kähler-Einstein metrics
moment polytopes
reduced Ding functional
ℚ-Fano compactifications of Lie groups

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10.1007/s10114-025-2511-4

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abstract = "Let G be a complex, connected reductive Lie group which is the complexification of a compact Lie group K. Let M be a ℚ-Fano G-compactification. In this paper, we first prove a uniqueness result of K × K-invariant (singular) K{\"a}hler–Einstein metrics on M. Then we show the existence of (singular) K{\"a}hler–Einstein metric implies properness of the reduced Ding functional. This gives a refinement of the properness conjecture on group compactifications.",

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T1 - Kähler–Einstein Metrics and Ding Functional on ℚ-Fano Group Compactifications

AU - Li, Yan

AU - Li, Zhenye

N1 - Publisher Copyright: © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2025.

PY - 2025/10

Y1 - 2025/10

N2 - Let G be a complex, connected reductive Lie group which is the complexification of a compact Lie group K. Let M be a ℚ-Fano G-compactification. In this paper, we first prove a uniqueness result of K × K-invariant (singular) Kähler–Einstein metrics on M. Then we show the existence of (singular) Kähler–Einstein metric implies properness of the reduced Ding functional. This gives a refinement of the properness conjecture on group compactifications.

AB - Let G be a complex, connected reductive Lie group which is the complexification of a compact Lie group K. Let M be a ℚ-Fano G-compactification. In this paper, we first prove a uniqueness result of K × K-invariant (singular) Kähler–Einstein metrics on M. Then we show the existence of (singular) Kähler–Einstein metric implies properness of the reduced Ding functional. This gives a refinement of the properness conjecture on group compactifications.

KW - 14L10

KW - 32Q20

KW - 53C25

KW - 58D25

KW - Kähler-Einstein metrics

KW - moment polytopes

KW - reduced Ding functional

KW - ℚ-Fano compactifications of Lie groups

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DO - 10.1007/s10114-025-2511-4

M3 - Article

AN - SCOPUS:105023908670

SN - 1439-8516

VL - 41

SP - 2555

EP - 2572

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 10

ER -

Kähler–Einstein Metrics and Ding Functional on ℚ-Fano Group Compactifications

Abstract

Keywords

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