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

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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 
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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     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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