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<p>We prove that an extremal metric on a polarised smooth complex projective variety exists if it is <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {G}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">G</mi> </math></EquationSource> </InlineEquation>-uniformly <i>K</i>-stable relative to the extremal torus over models, extending a result due to Chi Li (Ann Sci Ec Norm Super 55(6):1529–1574, 2022) for constant scalar curvature Kähler metrics.</p>

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Relative uniform K-stability over models implies existence of extremal metrics

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Yoshinori Hashimoto

摘要

We prove that an extremal metric on a polarised smooth complex projective variety exists if it is \(\mathbb {G}\) G -uniformly K-stable relative to the extremal torus over models, extending a result due to Chi Li (Ann Sci Ec Norm Super 55(6):1529–1574, 2022) for constant scalar curvature Kähler metrics.