A Non-Concentration Estimate for Partially Rectangular Billiards

Abstract

We consider quasimodes on planar domains with a partially rectangular boundary. We prove that for any ε0 > 0, an 𝒪(λ−ε0 ) quasimode must have L 2 mass in the “wings” (in phase space) bounded below by λ−2−δ for any δ > 0. The proof uses the author's recent work on 0-Gevrey smooth domains to approximate quasimodes on C 1, 1 domains. There is an improvement for C k, α and C ∞ domains.