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O(n) invariant solutions of Abreu's equation

A. N. W. Hone
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Abstract

We consider a fourth order partial differential equation in n-dimensional space introduced by Abreu in the context of Kähler metrics on toric orbifolds. Similarity solutions depending only on the radial coordinate in R^n are determined in terms of a second order ordinary differential equation. A local asymptotic analysis of solutions in the neighbourhood of singular points is carried out. The integrability (or otherwise) of Abreu's equation is discussed.

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A. N. W. Hone. 2002-09-11. O(n) invariant solutions of Abreu's equation. https://arxiv.org/abs/math/0209123

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