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

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

2004-10-07

arxiv.org/abs/math-ph/0410022v1

Physics

Mathematical Physics

Scientific paper

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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