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arXiv · 1908.09789

Uniqueness among scalar-flat Kähler metrics on non-compact toric $4$-manifolds

Rosa Sena-Dias
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Abstract

Abreu-Sena-Dias have constructed two distinct families of scalar-flat Kähler 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 Kähler metrics on any given strictly unbounded toric surface. We also show that the asymptotic behaviour of such a metric determines it uniquely.

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Rosa Sena-Dias. 2019-08-26. Uniqueness among scalar-flat Kähler metrics on non-compact toric $4$-manifolds. https://doi.org/10.1112/jlms.12377

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