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

Yaxiong Liu

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arXiv · 2004.12634

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

Yaxiong Liu

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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.

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BibTeX RIS

Yaxiong Liu. 2020-04-27. Uniform K-stability and Conformally K\"{a}hler, Einstein-Maxwell geometry on toric manifolds. https://arxiv.org/abs/2004.12634

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