On the existence and classification of $k$-Yamabe gradient solitons
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914969017122816 |
|---|---|
| author | Espinal, Maria Fernanda Sáez, Mariel |
| author_facet | Espinal, Maria Fernanda Sáez, Mariel |
| contents | In this paper we classify rotationally symmetric conformally flat admissible solitons to the $k$-Yamabe flow, a fully non-linear version of the Yamabe flow. For $n\geq 2k$ we prove existence of complete expanding, steady and shrinking solitons and describe their asymptotic behavior at infinity. For $n<2k$ we prove that steady and expanding solitons are not admissible. The proof is based on the careful analysis of an associated dynamical system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06942 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the existence and classification of $k$-Yamabe gradient solitons Espinal, Maria Fernanda Sáez, Mariel Differential Geometry 53C18, 53C21, 35C08, 58J60, 34A34 In this paper we classify rotationally symmetric conformally flat admissible solitons to the $k$-Yamabe flow, a fully non-linear version of the Yamabe flow. For $n\geq 2k$ we prove existence of complete expanding, steady and shrinking solitons and describe their asymptotic behavior at infinity. For $n<2k$ we prove that steady and expanding solitons are not admissible. The proof is based on the careful analysis of an associated dynamical system. |
| title | On the existence and classification of $k$-Yamabe gradient solitons |
| topic | Differential Geometry 53C18, 53C21, 35C08, 58J60, 34A34 |
| url | https://arxiv.org/abs/2410.06942 |