Relative uniform $K$-stability over models implies existence of extremal metrics
Differential Geometry
2026-04-09 v1 Algebraic Geometry
Abstract
We prove that an extremal metric on a polarised smooth complex projective variety exists if it is -uniformly -stable relative to the extremal torus over models, extending a result due to Chi Li for constant scalar curvature K\"ahler metrics.
Cite
@article{arxiv.2506.02360,
title = {Relative uniform $K$-stability over models implies existence of extremal metrics},
author = {Yoshinori Hashimoto},
journal= {arXiv preprint arXiv:2506.02360},
year = {2026}
}
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12 pages