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<p>In this note, we give a new proof for Perelman’s scalar curvature and diameter estimates for the Kähler-Ricci flow on Fano manifolds. The proof relies on a new Harnack estimate for a special family of functions in space-time. Our new approach initiates the work in Jian (Finite time singularities of the Kähler-Ricci flow, preprint) for general finite time solutions of the Kähler-Ricci flow.</p>

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A new proof of Perelman’s scalar curvature and diameter estimates for the Kähler-Ricci flow on Fano manifolds

  • 期刊论文

  • 发表日期：

    2026年5月16日

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  • Wangjian Jian,
  • Jian Song,
  • Gang Tian

摘要

In this note, we give a new proof for Perelman’s scalar curvature and diameter estimates for the Kähler-Ricci flow on Fano manifolds. The proof relies on a new Harnack estimate for a special family of functions in space-time. Our new approach initiates the work in Jian (Finite time singularities of the Kähler-Ricci flow, preprint) for general finite time solutions of the Kähler-Ricci flow.