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<p>The <i>H</i>-invariant was introduced to compute Perelmans entropy for Kähler–Ricci flow in a paper of Tian–Zhang–Zhang–Zhu more than ten years ago. It turns out that the <i>H</i>-invariant is equal to an earlier invariant by Tian–Zhu in their study on Kähler–Ricci solitons. In this largely expository paper, we will discuss definition of the <i>H</i>-invariant, its relation to Tian–Zhu’s generalization of the Futaki invariants as well as some of its applications. We will also include some new observations and generalizations of results in existing literature. Several examples will be also provided.</p>

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H-invariant and Its Applications

  • 期刊论文

  • 发表日期：

    2026年3月15日

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  • Gang Tian,
  • Xiaohua Zhu

摘要

The H-invariant was introduced to compute Perelmans entropy for Kähler–Ricci flow in a paper of Tian–Zhang–Zhang–Zhu more than ten years ago. It turns out that the H-invariant is equal to an earlier invariant by Tian–Zhu in their study on Kähler–Ricci solitons. In this largely expository paper, we will discuss definition of the H-invariant, its relation to Tian–Zhu’s generalization of the Futaki invariants as well as some of its applications. We will also include some new observations and generalizations of results in existing literature. Several examples will be also provided.