Skip to main content

Research Repository

Advanced Search

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

Klassert, S.; Lenz, D.; Peyerimhoff, N.; Stollmann, P.

Authors

S. Klassert

D. Lenz

P. Stollmann



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.

Citation

Klassert, S., Lenz, D., Peyerimhoff, N., & Stollmann, P. (2006). Elliptic operators on planar graphs: unique continuation for eigenfunctions and nonpositive curvature. Proceedings of the American Mathematical Society, 134(5), 1549-1559

Journal Article Type Article
Publication Date 2006
Journal Proceedings of the American Mathematical Society
Print ISSN 0002-9939
Publisher American Mathematical Society
Peer Reviewed Peer Reviewed
Volume 134
Issue 5
Pages 1549-1559