Green's function for the Laplace–Beltrami operator on a toroidal surface
2013 ◽
Vol 469
(2149)
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pp. 20120479
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Keyword(s):
Green's function for the Laplace–Beltrami operator on the surface of a three-dimensional ring torus is constructed. An integral ingredient of our approach is the stereographic projection of the torus surface onto a planar annulus. Our representation for Green's function is written in terms of the Schottky–Klein prime function associated with the annulus and the dilogarithm function. We also consider an application of our results to vortex dynamics on the surface of a torus.
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1967 ◽
Vol 22
(4)
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pp. 422-431
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2006 ◽
Vol 324-325
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pp. 387-390
2014 ◽
Vol 83
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pp. 155-162
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Keyword(s):
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2013 ◽
Vol 133
(5)
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pp. 3529-3529