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

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

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
• Electronic ISSN: 1088-6826
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 134
• Issue: 5
• Pages: 1549-1559
• Public URL: https://durham-repository.worktribe.com/output/1586404