Scalar curvature of self-shrinkers
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911694521892864 |
|---|---|
| author | Cheng, Qing-Ming Li, Fengjiang Wei, Guoxin |
| author_facet | Cheng, Qing-Ming Li, Fengjiang Wei, Guoxin |
| contents | In this paper, we study scalar curvature of $n$-dimensional self-shrinkers in the Euclidean space $\mathbb R^{n+1}$. If the scalar curvature of an $n$-dimensional self-shrinker is a positive constant, then we prove that the scalar curvature $R$ satisfies $0<R\leq n-1$. Furthermore, we classify $n$-dimensional complete self-shrinkers in $\mathbb R^{n+1}$ with non-negative constant scalar curvature. We also study $n$-dimensional complete self-shrinkers in $\mathbb R^{n+1}$ with constant squared norm of the second fundamental form $S$. We partially resolve the conjecture on $n$-dimensional complete self-shrinkers in $\mathbb R^{n+1}$ with constant squared norm $S$ of the second fundamental form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18532 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scalar curvature of self-shrinkers Cheng, Qing-Ming Li, Fengjiang Wei, Guoxin Differential Geometry In this paper, we study scalar curvature of $n$-dimensional self-shrinkers in the Euclidean space $\mathbb R^{n+1}$. If the scalar curvature of an $n$-dimensional self-shrinker is a positive constant, then we prove that the scalar curvature $R$ satisfies $0<R\leq n-1$. Furthermore, we classify $n$-dimensional complete self-shrinkers in $\mathbb R^{n+1}$ with non-negative constant scalar curvature. We also study $n$-dimensional complete self-shrinkers in $\mathbb R^{n+1}$ with constant squared norm of the second fundamental form $S$. We partially resolve the conjecture on $n$-dimensional complete self-shrinkers in $\mathbb R^{n+1}$ with constant squared norm $S$ of the second fundamental form. |
| title | Scalar curvature of self-shrinkers |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.18532 |