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Uniqueness among scalar-flat K\"ahler metrics on non-compact toric $4$-manifolds

Differential Geometry 2020-10-07 v1

Abstract

Abreu-Sena-Dias have constructed two distinct families of scalar-flat K\"ahler non-compact toric metrics using Donaldson's rephrasing of Joyce's construction in action-angle coordinates. In this paper and using the same set-up, we show that these are the only J-complete scalar-flat K\"ahler metrics on any given strictly unbounded toric surface. We also show that the asymptotic behaviour of such a metric determines it uniquely.

Keywords

Cite

@article{arxiv.1908.09789,
  title  = {Uniqueness among scalar-flat K\"ahler metrics on non-compact toric $4$-manifolds},
  author = {Rosa Sena-Dias},
  journal= {arXiv preprint arXiv:1908.09789},
  year   = {2020}
}

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23 pages