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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- Last edited by John Jones on 2012-06-26 14:33:49

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- 2012-06-26 14:33:49 by John Jones (Reviewed)