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Quasimode concentration on compact space forms
Published 21 Apr 2024 in math.AP, math.CA, and math.DG | (2404.13738v1)
Abstract: We show that the upper bounds for the $L2$-norms of $L1$-normalized quasimodes that we obtained in [9] are always sharp on any compact space form. This allows us to characterize compact manifolds of constant sectional curvature using the decay rates of lower bounds of $L1$-norms of $L2$-normalized log-quasimodes fully resolving a problem initiated by the second author and Zelditch [15]. We are also able to characterize such manifolds by the concentration of quasimodes near periodic geodesics as measured by $L2$-norms over thin geodesic tubes.
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