Curvature and harmonic analysis on compact manifolds
| Autor: | Sogge, Christopher D. |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We discuss problems that relate curvature and concentration properties of eigenfunctions and quasimodes on compact boundaryless Riemannian manifolds. These include new sharp $L^q$-estimates, $q\in (2,q_c]$, $q_c=2(n+1)/(n-1)$, of log-quasimodes that characterize compact connected space forms in terms of the growth rate of $L^q$-norms of such quasimode for these relatively small Lebesgue exponents $q$. No such characterization is possible for any exponent $q> q_c$. Comment: 5 pages. To appear in ICBS proceedings |
| Databáze: | arXiv |
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