Sharp bounds for the intersection of nodal lines with certain curves

  • Junehyuk Jung

    Princeton University, USA

Abstract

Let be a hyperbolic surface and let be a Laplacian eigenfunction having eigenvalue with . Let be the set of nodal lines of . For a fixed analytic curve of finite length, we study the number of intersections between and in terms of . When is compact and a geodesic circle, or when has finite volume and is a closed horocycle, we prove that is ``good'' in the sense of \cite{pa}. As a result, we obtain that the number of intersections between and is . This bound is sharp.

Cite this article

Junehyuk Jung, Sharp bounds for the intersection of nodal lines with certain curves. J. Eur. Math. Soc. 16 (2014), no. 2, pp. 273–288

DOI 10.4171/JEMS/433