| Title:
|
A universal bound for lower Neumann eigenvalues of the Laplacian (English) |
| Author:
|
Lu, Wei |
| Author:
|
Mao, Jing |
| Author:
|
Wu, Chuanxi |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
2 |
| Year:
|
2020 |
| Pages:
|
473-482 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $M$ be an $n$-dimensional ($n\ge 2$) simply connected Hadamard manifold. If the radial Ricci curvature of $M$ is bounded from below by $(n-1)k(t)$ with respect to some point $p\in M$, where $t=d(\cdot ,p)$ is the Riemannian distance on $M$ to $p$, $k(t)$ is a nonpositive continuous function on $(0,\infty )$, then the first $n$ nonzero Neumann eigenvalues of the Laplacian on the geodesic ball $B(p,l)$, with center $p$ and radius $0<l<\infty $, satisfy $$ \frac {1}{\mu _1}+\frac {1}{\mu _2}+\cdots +\frac {1}{\mu _n}\ge \frac {l^{n+2}}{(n+2)\int _{0}^{l}f^{n-1}(t){\rm d}t}, $$ where $f(t)$ is the solution to $$ \begin {cases} f''(t)+k(t)f(t)=0 \quad \text {on} \ (0,\infty ),\\ f(0)=0, \ f'(0)=1. \end {cases} $$ (English) |
| Keyword:
|
Hadamard manifold |
| Keyword:
|
Neumann eigenvalue |
| Keyword:
|
radial Ricci curvature |
| MSC:
|
35P15 |
| MSC:
|
53C20 |
| idZBL:
|
07217146 |
| idMR:
|
MR4111854 |
| DOI:
|
10.21136/CMJ.2019.0363-18 |
| . |
| Date available:
|
2020-06-17T12:35:03Z |
| Last updated:
|
2022-07-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148240 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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