Uniform K-stability and Conformally K "ahler, Einstein-Maxwell\n geometry on toric manifolds

2020/04/27 by Yaxiong Liu, Liu, Yaxiong
Mathematics · Social Sciences · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.2004.12634

openalex publication_date 2020/04/27 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

Conformally K "ahler, Einstein-Maxwell metrics and f-extremal metrics are\ngeneralization of canonical metrics in K "ahler geometry. We introduce\nuniform K-stability for toric K "ahler manifolds, and show that uniform\nK-stability is necessary condition for the existence of f-extremal metrics on\ntoric manifolds. Furthermore, we show that uniform K-stability is equivalent to\nproperness of relative K-energy.\n

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