On the Geometry of the Nodal Lines of Eigenfunctions of the Two-Dimensional Torus

Details On the Geometry of the Nodal Lines of Eigenfunctions of the Two-Dimensional Torus On the Geometry of the Nodal Lines of Eigenfunctions of the Two-Dimensional Torus

2010-12-17

arxiv.org/abs/1012.3843v2

Mathematics

Analysis of PDEs

4 figures. Added some comments about total curvature and other details

Scientific paper

The width of a convex curve in the plane is the minimal distance between a pair of parallel supporting lines of the curve. In this paper we study the width of nodal lines of eigenfunctions of the Laplacian on the standard flat torus. We prove a variety of results on the width, some having stronger versions assuming a conjecture of Cilleruelo and Granville asserting a uniform bound for the number of lattice points on the circle lying in short arcs.

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