Curvature and harmonic analysis on compact manifolds
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914764151586816 |
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| author | Sogge, Christopher D. |
| author_facet | Sogge, Christopher D. |
| contents | 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 $q> q_c$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13739 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Curvature and harmonic analysis on compact manifolds Sogge, Christopher D. Analysis of PDEs Classical Analysis and ODEs Differential Geometry 58J50, 35P15 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 $q> q_c$. |
| title | Curvature and harmonic analysis on compact manifolds |
| topic | Analysis of PDEs Classical Analysis and ODEs Differential Geometry 58J50, 35P15 |
| url | https://arxiv.org/abs/2404.13739 |