| Title:
|
Monotonicity of first eigenvalues along the Yamabe flow (English) |
| Author:
|
Zhang, Liangdi |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
387-401 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We construct some nondecreasing quantities associated to the first eigenvalue of $-\Delta _\phi +cR$ $(c\geq \frac 12(n-2)/(n-1))$ along the Yamabe flow, where $\Delta _\phi $ is the Witten-Laplacian operator with a $C^2$ function $\phi $. We also prove a monotonic result on the first eigenvalue of $-\Delta _\phi + \frac 14 (n/ (n-1))R$ along the Yamabe flow. Moreover, we establish some nondecreasing quantities for the first eigenvalue of $-\Delta _\phi +cR^a$ with $a\in (0,1)$ along the Yamabe flow. (English) |
| Keyword:
|
monotonicity |
| Keyword:
|
first eigenvalue |
| Keyword:
|
Witten-Laplacian operator |
| Keyword:
|
Yamabe flow |
| MSC:
|
58C40 |
| idZBL:
|
07361075 |
| idMR:
|
MR4263176 |
| DOI:
|
10.21136/CMJ.2020.0392-19 |
| . |
| Date available:
|
2021-05-20T13:41:37Z |
| Last updated:
|
2023-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148911 |
| . |
| Reference:
|
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