Special Kähler structures, cubic differentials and hyperbolic metrics

@article{Haydys2018SpecialKS,
  title={Special K{\"a}hler structures, cubic differentials and hyperbolic metrics},
  author={Andriy Haydys and Bin Xu},
  journal={Selecta Mathematica},
  year={2018},
  volume={26},
  pages={1-21}
}
We obtain necessary conditions for the existence of special Kähler structures with isolated singularities on compact Riemann surfaces. We prove that these conditions are also sufficient in the case of the Riemann sphere and, moreover, we determine the whole moduli space of special Kähler structures with fixed singularities. The tool we develop for this aim is a correspondence between special Kähler structures and pairs consisting of a cubic differential and a hyperbolic metric. 
Twisted and Singular Gravitating Vortices
  • Chengjian Yao
  • Mathematics, Physics
  • The Journal of Geometric Analysis
  • 2021
We introduce the notion of twisted gravitating vortex on a compact Riemann surface. If the genus of the Riemann surface is greater than 1 and the twisting forms have suitable signs, we prove anExpand

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