O(n) invariant solutions of Abreu's equation
A. N. W. Hone
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 Rn 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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