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<p>Let <i>G</i> be a complex, connected reductive Lie group which is the complexification of a compact Lie group <i>K</i>. Let <i>M</i> be a ℚ-Fano <i>G</i>-compactification. In this paper, we first prove a uniqueness result of <i>K</i> × <i>K</i>-invariant (singular) Kähler–Einstein metrics on <i>M</i>. 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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年10月15日

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  • Yan Li,
  • Zhenye Li

摘要

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.