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March 2004 Solutions of Abreu's Equation with Rotation Invariance
A. N. W. Hone
Methods Appl. Anal. 11(1): 041-064 (March 2004).


We consider a fourth order nonlinear partial differential equation in n-dimensional space introduced by Abreu in the context of Kahler metrics on toric varieties. Rotation invariant similarity solutions, depending only on the radial coordinate in Rn, are determined from the solutions of a second order ordinary differential equation (ODE), with a non-autonomous Lagrangian formulation. A local asymptotic analysis of solutions of the ODE in the neighbourhood of singular points is carried out, and the existence of a class of solutions on an interval of the positive real semi-axis is proved using a nonlinear integral equation. The integrability (or otherwise) of Abreu's equation is discussed.


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A. N. W. Hone. "Solutions of Abreu's Equation with Rotation Invariance." Methods Appl. Anal. 11 (1) 041 - 064, March 2004.


Published: March 2004
First available in Project Euclid: 15 June 2005

zbMATH: 1091.53021
MathSciNet: MR2128350

Rights: Copyright © 2004 International Press of Boston


Vol.11 • No. 1 • March 2004
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