To obtain the representation of \(\Delta\) in polar coordinates mentioned in (0x691b343c) one use polar coordinates, calculate the metric tensor and plug it in into the local representation of the Laplace-Beltrami operator, e.g. see [1].

Links Link to heading

• Laplacian in polar coordinates
• Laplacian in polar coordinates wrt \(\mathbb{S}^d_R\)

References Link to heading

1. J. Gallier. Class Lecture, Topic: Notes on Spherical Harmonics and Linear Representations of Lie Groups.