Current browse context:
math.AP
Change to browse by:
References & Citations
Mathematics > Analysis of PDEs
Title: Quasimode concentration on compact space forms
(Submitted on 21 Apr 2024)
Abstract: We show that the upper bounds for the $L^2$-norms of $L^1$-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 $L^1$-norms of $L^2$-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 $L^2$-norms over thin geodesic tubes.
Link back to: arXiv, form interface, contact.