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Some harmonic functions on Minkowski space

Author(s): P. F. Glezen; R. C. Penner
Journal: Proc. Amer. Math. Soc. 125 (1997), 1659-1665.
MSC (1991): Primary 30Cxx, 30Fxx
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Abstract: This note presents elementary geometric descriptions of several simple families of harmonic functions on the upper sheet of the unit hyperboloid in Minkowski three-space. As is briefly discussed here, these calculations grew out of an earlier attempt to construct Poincaré series on punctured surfaces using Minkowski geometry.

References:

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[P1]: R. C. Penner, The decorated Teichmüller space of punctured surfaces, Comm. Math. Phys. 113 (1987), 299-339. MR 89h:32044
[P2]: -, Calculus on moduli space, Contemp. Math. 74 (1988), 277-293. MR 90a:32029
[P3]: -, An arithmetic problem in surface geometry, The Moduli Space of Curves (Texel Island, 1994), Progr. Math., vol. 129, Birkhäuser, Boston, MA, 1995, pp. 427-466. CMP 96:04


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