| Title:
|
A note on the nonexistence of spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form (English) |
| Author:
|
de Lima, Henrique Fernandes |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
58 |
| Issue:
|
3 |
| Year:
|
2022 |
| Pages:
|
169-175 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We obtain nonexistence results concerning complete noncompact spacelike hypersurfaces with polynomial volume growth immersed in a Lorentzian space form, under the assumption that the support functions with respect to a fixed nonzero vector are linearly related. Our approach is based on a suitable maximum principle recently established by Alías, Caminha and do Nascimento [3]. (English) |
| Keyword:
|
Lorentzian space forms |
| Keyword:
|
complete spacelike hypersurfaces |
| Keyword:
|
polynomial volume growth |
| Keyword:
|
support functions |
| MSC:
|
53C42 |
| MSC:
|
53C50 |
| idZBL:
|
Zbl 07584088 |
| idMR:
|
MR4483051 |
| DOI:
|
10.5817/AM2022-3-169 |
| . |
| Date available:
|
2022-09-01T10:19:28Z |
| Last updated:
|
2023-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150662 |
| . |
| Reference:
|
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| Reference:
|
[2] Alías, L.J., Brasil Jr., A., Perdomo, O.: A characterization of quadric constant mean curvature hypersurfaces of spheres.J. Geom. Anal. 18 (2008), 687–703. MR 2420759, 10.1007/s12220-008-9029-8 |
| Reference:
|
[3] Alías, L.J., Caminha, A., do Nascimento, F.Y.: A maximum principle related to volume growth and applications.Ann. Mat. Pura Appl. 200 (2021), 1637–1650. MR 4278219 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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