Some harmonic functions on Minkowski space

Authors:
P. F. Glezen and R. C. Penner

Journal:
Proc. Amer. Math. Soc. **125** (1997), 1659-1665

MSC (1991):
Primary 30Cxx, 30Fxx

MathSciNet review:
1346976

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Abstract | References | Similar Articles | Additional Information

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.

**[EP]**D. B. A. Epstein and R. C. Penner,*Euclidean decompositions of noncompact hyperbolic manifolds*, J. Differential Geom.**27**(1988), no. 1, 67–80. MR**918457****[P1]**R. C. Penner,*The decorated Teichmüller space of punctured surfaces*, Comm. Math. Phys.**113**(1987), no. 2, 299–339. MR**919235****[P2]**R. C. Penner,*Calculus on moduli space*, Geometry of group representations (Boulder, CO, 1987) Contemp. Math., vol. 74, Amer. Math. Soc., Providence, RI, 1988, pp. 277–293. MR**957525**, 10.1090/conm/074/957525**[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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Additional Information

**P. F. Glezen**

Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, California 90089

Address at time of publication:
ISSC, Inc., One Market Plaza, San Francisco, California 94105

**R. C. Penner**

Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, California 90089

Email:
rpenner@mathi.usc.edu

DOI:
https://doi.org/10.1090/S0002-9939-97-03545-4

Received by editor(s):
April 7, 1995

Additional Notes:
The second author was partially supported by the National Science Foundation

Communicated by:
Peter Li

Article copyright:
© Copyright 1997
American Mathematical Society