| Title:
|
Functional inequalities and manifolds with nonnegative weighted Ricci curvature (English) |
| Author:
|
Mao, Jing |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
213-233 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that $n$-dimensional $(n\geqslant 2)$ complete and noncompact metric measure spaces with nonnegative weighted Ricci curvature in which some Caffarelli-Kohn-Nirenberg type inequality holds are isometric to the model metric measure $n$-space (i.e. the Euclidean metric $n$-space). We also show that the Euclidean metric spaces are the only complete and noncompact metric measure spaces of nonnegative weighted Ricci curvature satisfying some prescribed Sobolev type inequality. (English) |
| Keyword:
|
Caffarelli-Kohn-Nirenberg type inequality |
| Keyword:
|
weighted Ricci curvature |
| Keyword:
|
volume comparison |
| MSC:
|
31C12 |
| MSC:
|
53C21 |
| idZBL:
|
07217130 |
| idMR:
|
MR4078355 |
| DOI:
|
10.21136/CMJ.2019.0214-18 |
| . |
| Date available:
|
2020-03-10T10:18:25Z |
| Last updated:
|
2022-04-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148051 |
| . |
| Reference:
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