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Register a new userUnique Continuation for Quasimodes on Surfaces of Revolution: Rotationally invariant Neighbourhoods
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Hans Christianson
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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 $L^2$ mass bounded below by $C_epsilon lambda^{-1 - epsilon}$ for any $epsilon>0$ 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 $C_delta lambda^{-1 + delta}$ for some fixed $delta>0$.
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