A non-concentration estimate for partially rectangular billiards

Original · EN

We consider quasimodes on planar domains with a partially rectangular boundary. We prove that for any ε₀>0, an Ø(λ⁻ε⁰) quasimode must have L² mass in the "wings" 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 C¹,¹ domains. There is an improvement for C²,α domains.