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arXiv · 2506.02360

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

Yoshinori Hashimoto
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Abstract

We prove that an extremal metric on a polarised smooth complex projective variety exists if it is $\mathbb{G}$-uniformly $K$-stable relative to the extremal torus over models, extending a result due to Chi Li for constant scalar curvature K\"ahler metrics.

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Yoshinori Hashimoto. 2025-06-03. Relative uniform $K$-stability over models implies existence of extremal metrics. https://doi.org/10.1007/s00209-026-04014-7

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