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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: October 25, 2005
MathSciNet review: 2199204
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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 $ (3,6), (4,4)$ and $ (6,3)$ tilings.


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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
Published electronically: October 25, 2005
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.