# Sharp bounds for the intersection of nodal lines with certain curves

Journal of the European Mathematical Society (2014)

- Volume: 016, Issue: 2, page 273-288
- ISSN: 1435-9855

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topJung, Junehyuk. "Sharp bounds for the intersection of nodal lines with certain curves." Journal of the European Mathematical Society 016.2 (2014): 273-288. <http://eudml.org/doc/277180>.

@article{Jung2014,

abstract = {Let $Y$ be a hyperbolic surface and let $\phi $ be a Laplacian eigenfunction having eigenvalue $-1/4-\tau ^2$ with $\tau >0$. Let $N(\phi )$ be the set of nodal lines of $\phi $. For a fixed analytic curve $\gamma $ of finite length, we study the number of intersections between $N(\phi )$ and $\gamma $ in terms of $\tau $. When $Y$ is compact and $\gamma $ a geodesic circle, or when $Y$ has finite volume and $\gamma $ is a closed horocycle, we prove that $\gamma $ is “good” in the sense of [TZ]. As a result, we obtain that the number of intersections between $N(\phi )$ and $\gamma $ is $O(\tau )$. This bound is sharp.},

author = {Jung, Junehyuk},

journal = {Journal of the European Mathematical Society},

keywords = {nodal domain; hyperbolic surfaces; eigenfunctions; Laplacian; geodesic circle; hyperbolic surface; Laplacian; geodesic circle; eigenvalue},

language = {eng},

number = {2},

pages = {273-288},

publisher = {European Mathematical Society Publishing House},

title = {Sharp bounds for the intersection of nodal lines with certain curves},

url = {http://eudml.org/doc/277180},

volume = {016},

year = {2014},

}

TY - JOUR

AU - Jung, Junehyuk

TI - Sharp bounds for the intersection of nodal lines with certain curves

JO - Journal of the European Mathematical Society

PY - 2014

PB - European Mathematical Society Publishing House

VL - 016

IS - 2

SP - 273

EP - 288

AB - Let $Y$ be a hyperbolic surface and let $\phi $ be a Laplacian eigenfunction having eigenvalue $-1/4-\tau ^2$ with $\tau >0$. Let $N(\phi )$ be the set of nodal lines of $\phi $. For a fixed analytic curve $\gamma $ of finite length, we study the number of intersections between $N(\phi )$ and $\gamma $ in terms of $\tau $. When $Y$ is compact and $\gamma $ a geodesic circle, or when $Y$ has finite volume and $\gamma $ is a closed horocycle, we prove that $\gamma $ is “good” in the sense of [TZ]. As a result, we obtain that the number of intersections between $N(\phi )$ and $\gamma $ is $O(\tau )$. This bound is sharp.

LA - eng

KW - nodal domain; hyperbolic surfaces; eigenfunctions; Laplacian; geodesic circle; hyperbolic surface; Laplacian; geodesic circle; eigenvalue

UR - http://eudml.org/doc/277180

ER -

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