Periodic solutions of Abreu's equation
Renjie Feng, G\'abor Sz\'ekelyhidi
TL;DR
This paper solves Abreu's equation with periodic right hand side in any dimension, providing a method to prescribe scalar curvature for torus-invariant metrics on Abelian varieties.
Contribution
It introduces a solution to Abreu's equation with periodic data, extending the understanding of scalar curvature prescription on Abelian varieties.
Findings
Solution to Abreu's equation with periodic right hand side in all dimensions
Application to scalar curvature prescription on Abelian varieties
Advancement in geometric analysis of torus-invariant metrics
Abstract
We solve Abreu's equation with periodic right hand side, in any dimension. This can be interpreted as prescribing the scalar curvature of a torus invariant metric on an Abelian variety.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Meromorphic and Entire Functions