Gradient estimate of an eigenfunction on a compact Riemannian manifold without boundary
| dc.creator | Shi, Yiqian | |
| dc.creator | Xu, Bin | |
| dc.date | 2009-05-09 | |
| dc.date | 2009-05-21 | |
| dc.date.accessioned | 2026-07-07T13:16:43Z | |
| dc.date.available | 2026-07-07T13:16:43Z | |
| dc.description | Let $e_ł(x)$ be an eigenfunction with respect to the Laplace-Beltrami operator $Δ_M$ on a compact Riemannian manifold $M$ without boundary: $Δ_M e_ł=ł^2 e_ł$. We show the following gradient estimate of $e_ł$: for every $ł\geq 1$, there holds $ł\|e_ł\|_\infty/C\leq \|\nabla e_ł\|_\infty\leq Cł\|e_ł\|_\infty$, where $C$ is a positive constant depending only on $M$. | |
| dc.description | 8 pages. The abstract is shortened to two sentences. The reference of the book by Yu Safarov and D. Vassiliev was added. An alternative proof of the gradient estimate for the unit band spectral projection operator is added in Section 4. The layout is changed | |
| dc.identifier | https://arxiv.org/abs/0905.1366 | |
| dc.identifier | http://arxiv.org/abs/0905.1366 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230879 | |
| dc.subject | Spectral Theory | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35P20; 35J05 | |
| dc.title | Gradient estimate of an eigenfunction on a compact Riemannian manifold without boundary | |
| dc.type | text |