Zeros of eigenfunctions on hyperbolic surfaces lying on a curve

Details Zeros of eigenfunctions on hyperbolic surfaces lying on a curve Zeros of eigenfunctions on hyperbolic surfaces lying on a curve

2011-08-11

arxiv.org/abs/1108.2335v2

Mathematics

Differential Geometry

22 pages

Scientific paper

We study the number of intersection between the nodal set of a Laplacian
eigenfunction on a hyperbolic surface and a fixed analytic segment on the
surface in terms of the eigenvalue. We give a sharp upper bound for this number
when the curve is a closed horocycle on a hyperbolic surface of finite volume,
or a geodesic circle on a compact hyperbolic surface.

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