Uniform K-stability and Conformally K\"{a}hler, Einstein-Maxwell geometry on toric manifolds

Yaxiong Liu

Uniform K-stability and Conformally K\"{a}hler, Einstein-Maxwell geometry on toric manifolds

Differential Geometry 2022-08-09 v2

Authors: Yaxiong Liu

Abstract

Conformally K\"{a}hler, Einstein-Maxwell metrics and $f$ -extremal metrics are generalization of canonical metrics in K\"{a}hler geometry. We introduce uniform K-stability for toric K\"{a}hler manifolds, and show that uniform K-stability is necessary condition for the existence of $f$ -extremal metrics on toric manifolds. Furthermore, we show that uniform K-stability is equivalent to properness of relative K-energy.

Keywords

uniform k-stability toric kähler manifolds f-extremal metrics conformally kähler einstein-maxwell metrics relative k-energy

Cite

@article{arxiv.2004.12634,
  title  = {Uniform K-stability and Conformally K\"{a}hler, Einstein-Maxwell geometry on toric manifolds},
  author = {Yaxiong Liu},
  journal= {arXiv preprint arXiv:2004.12634},
  year   = {2022}
}

Comments

published in Tohoku Math. J. arXiv admin note: text overlap with arXiv:1109.5228, arXiv:1512.06391 by other authors

Uniform K-stability and Conformally K\"{a}hler, Einstein-Maxwell geometry on toric manifolds

Abstract

Keywords

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