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Elliptic operators on planar graphs: Unique continuation for eigenfunctions and nonpositive curvature

Author(s): Steffen Klassert; Daniel Lenz; Norbert Peyerimhoff; Peter Stollmann
Journal: Proc. Amer. Math. Soc. 134 (2006), 1549-1559.
MSC (2000): Primary 58J50, 35J10; Secondary 81Q10
Posted: October 25, 2005
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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: 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
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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