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MR1981450 83C45 (53C80)
Akbar, M. M.; Gibbons, G. W. Ricci-flat metrics with ${\rm U}(1)$ action and Dirichlet boundary-value problem in Riemannian quantum gravity and isoperimetric inequalities. Classical Quantum Gravity 20 (2003), no. 9, 1787–1822.
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