| Title:
|
Conformal Killing graphs in foliated Riemannian spaces with density: rigidity and stability (English) |
| Author:
|
Velásquez, Marco L. A. |
| Author:
|
Ramalho, André F. A. |
| Author:
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de Lima, Henrique F. |
| Author:
|
Santos, Márcio S. |
| Author:
|
Oliveira, Arlandson M. S. |
| Language:
|
English |
| Journal:
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Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
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0010-2628 (print) |
| ISSN:
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1213-7243 (online) |
| Volume:
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62 |
| Issue:
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2 |
| Year:
|
2021 |
| Pages:
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175-200 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we investigate the geometry of conformal Killing graphs in a Riemannian manifold $\overline{M}_f^{ n+1}$ endowed with a weight function $f$ and having a closed conformal Killing vector field $V$ with conformal factor $\psi_V$, that is, graphs constructed through the flow generated by $V$ and which are defined over an integral leaf of the foliation $V^{\perp}$ orthogonal to $V$. For such graphs, we establish some rigidity results under appropriate constraints on the $f$-mean curvature. Afterwards, we obtain some stability results for $f$-minimal conformal Killing graphs of $ \overline{M}_f^{ n+1}$ according to the behavior of $ \psi_V$. Finally, related to conformal Killing graphs immersed in $\overline{M}_f^{n+1}$ with constant $f$-mean curvature, we study the strong stability. (English) |
| Keyword:
|
weighted Riemannian manifold |
| Keyword:
|
conformal Killing graph |
| Keyword:
|
$f$-mean curvature |
| Keyword:
|
Bakry--Émery--Ricci tensor |
| Keyword:
|
strong $f$-stability |
| MSC:
|
53C42 |
| idZBL:
|
Zbl 07396218 |
| idMR:
|
MR4303577 |
| DOI:
|
10.14712/1213-7243.2021.017 |
| . |
| Date available:
|
2021-07-28T08:36:18Z |
| Last updated:
|
2023-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149011 |
| . |
| Reference:
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