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Elliptic operators on planar graphs: Unique continuation for eigenfunctions and nonpositive curvature
Authors:
Steffen Klassert, Daniel Lenz, Norbert Peyerimhoff and Peter Stollmann
Journal:
Proc. Amer. Math. Soc. 134 (2006), 1549-1559
MSC (2000):
Primary 58J50, 35J10; Secondary 81Q10
Posted:
October 25, 2005
MathSciNet review:
2199204
Full-text PDF Free Access
Abstract |
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Additional Information
Abstract: This paper is concerned with elliptic operators on plane tessellations. We show that such an operator does not admit a compactly supported eigenfunction if the combinatorial curvature of the tessellation is nonpositive. Furthermore, we show that the only geometrically finite, repetitive plane tessellations with nonpositive curvature are the regular  and  tilings.
References
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Additional Information
Steffen Klassert
Affiliation:
Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany
Email:
S.Klassert@mathematik.tu-chemnitz.de
Daniel Lenz
Affiliation:
Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany
Email:
D.Lenz@mathematik.tu-chemnitz.de
Norbert Peyerimhoff
Affiliation:
Department of Mathematical Sciences, University of Durham, South Road, Durham DH1 3LE, England
Email:
norbert.peyerimhoff@durham.ac.uk
Peter Stollmann
Affiliation:
Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany
Email:
P.Stollmann@mathematik.tu-chemnitz.de
DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08103-7
PII:
S 0002-9939(05)08103-7
Received by editor(s):
December 24, 2004
Posted:
October 25, 2005
Communicated by:
Jozef Dodziuk
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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