Elliptic operators on planar graphs: Unique continuation for eigenfunctions and nonpositive curvature
S. Klassert, D. Lenz, N. Peyerimhoff, 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.
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