Autor:	Huang, Xiaoqi, Sogge, Christopher D.
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs Mathematics - Classical Analysis and ODEs Mathematics - Differential Geometry 58J50 35P15
Druh dokumentu:	Working Paper
Popis:	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. Comment: 16 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.13738 Zobrazit plný text záznamu View this record from Arxiv