Unique Continuation for Quasimodes on Surfaces of Revolution: Rotationally invariant Neighbourhoods

الأصل · EN

We prove a strong conditional unique continuation estimate for irreducible quasimodes in rotationally invariant neighbourhoods on compact surfaces of revolution. The estimate states that Laplace quasimodes which cannot be decomposed as a sum of other quasimodes have L² mass bounded below by Cελ⁻¹ ⁻ ε for any ε>0 on any open rotationally invariant neighbourhood which meets the semiclassical wavefront set of the quasimode. For an analytic manifold, we conclude the same estimate with a lower bound of Cδλ⁻¹ ⁺ δ for some fixed δ>0.