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<p>We show that for a broad family of noncompact homogeneous Riemannian manifolds, the corresponding homogeneous Ricci flow solutions have finite extinction time, thereby confirming the dynamical Alekseevskii conjecture for these spaces. As an application, we prove that on such homogeneous manifolds <i>G</i>/<i>H</i>, the space of all <i>G</i>-invariant positive scalar curvature metrics is contractible.</p>

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Finite extinction time of a family of homogeneous Ricci flows

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Roberto Araujo

摘要

We show that for a broad family of noncompact homogeneous Riemannian manifolds, the corresponding homogeneous Ricci flow solutions have finite extinction time, thereby confirming the dynamical Alekseevskii conjecture for these spaces. As an application, we prove that on such homogeneous manifolds G/H, the space of all G-invariant positive scalar curvature metrics is contractible.