Geodesic
Sharp bounds for the intersection of nodal lines with certain curves
Journal of the European Mathematical Society, Tome 16 (2014) no. 2, pp. 273-288 Cet article a éte moissonné depuis la source EMS Press

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Let Y be a hyperbolic surface and let φ be a Laplacian eigenfunction having eigenvalue −1/4−τ2 with τ>0. Let N(φ) be the set of nodal lines of φ. For a fixed analytic curve γ of finite length, we study the number of intersections between N(φ) and γ in terms of τ. When Y is compact and γ a geodesic circle, or when Y has finite volume and γ is a closed horocycle, we prove that γ is “good” in the sense of [TZ]. As a result, we obtain that the number of intersections between N(φ) and γ is O(τ). This bound is sharp.
DOI : 10.4171/jems/433
Classification : 53-XX, 32-XX, 33-XX, 78-XX
Keywords: Nodal domain, hyperbolic surfaces, eigenfunctions 
@article{JEMS_2014_16_2_a2,
     author = {Junehyuk Jung},
     title = {Sharp bounds for the intersection of nodal lines with certain curves},
     journal = {Journal of the European Mathematical Society},
     pages = {273--288},
     year = {2014},
     volume = {16},
     number = {2},
     doi = {10.4171/jems/433},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/433/}
}
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Junehyuk Jung. Sharp bounds for the intersection of nodal lines with certain curves. Journal of the European Mathematical Society, Tome 16 (2014) no. 2, pp. 273-288. doi: 10.4171/jems/433

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