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The Laplace-Beltrami operator on the hyperbolic upper half-plane is given by $$\Delta = -y^{2} \left(\frac{\partial^{2}}{\partial x^{2}}+\frac{\partial^{2}}{\partial y^{2}}\right).$$ Note that it is sometimes defined without the minus sign in front.

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• Review status: reviewed
• Last edited by John Jones on 2012-06-26 14:33:49
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