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Let Ω ⊂ R 2 be a bounded piecewise smooth domain and ϕ λ be a Neumann (or Dirichlet) eigenfunction with eigenvalue λ 2 and nodal set N ϕ λ = {x ∈ Ω; ϕ λ (x) = 0}. Let H ⊂ Ω be an interior C ω curve. Consider the intersection numberWe first prove that for general piecewise-analytic domains, and under an appropriate "goodness" condition on H (see Theorem 1.1),as λ → ∞. Then, using Theorem 1.1, we prove in Theorem 1.2 that the bound in (1) is satisfied in the case of quantum ergodic (QE) sequences of interior eigenfunctions, provided Ω is convex and H has strictly positive geodesic curvature.

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