2024/04/21 by Huang, Xiaoqi, Sogge, Christopher D. · 1 citation
#35P15 #58J50 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2404.13738
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.