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Elliptic operators on planar graphs: Unique continuation for eigenfunctions and nonpositive curvature |
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| Authors: | Steffen Klassert Daniel Lenz Norbert Peyerimhoff Peter Stollmann |
| Affiliation: | Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany ; Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany ; Department of Mathematical Sciences, University of Durham, South Road, Durham DH1 3LE, England ; Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany |
| 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. |
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