Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2401.03387 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913188318019584 |
|---|---|
| author | Chan, Pak-Yeung Ma, Zilu Zhang, Yongjia |
| author_facet | Chan, Pak-Yeung Ma, Zilu Zhang, Yongjia |
| contents | A noncollapsed $\mathbb{F}$-limit metric soliton is a self-similar singularity model that inevitably arises when studying the Ricci flow with the tool of $\mathbb{F}$-convergence [Bam20a,Bam20b,Bam20c]. In this article, we shall present a systematic study of the noncollapsed $\mathbb{F}$-limit metric soliton, and show that, apart from the known results in [Bam20c], it satisfies many properties of smooth Ricci shrinkers. In particular, we show a quadratic lower bound for the scalar curvature, a local gap theorem, a global Sobolev inequality, and an optimal volume growth lower bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03387 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On noncollapsed $\mathbb{F}$-limit metric solitons Chan, Pak-Yeung Ma, Zilu Zhang, Yongjia Differential Geometry A noncollapsed $\mathbb{F}$-limit metric soliton is a self-similar singularity model that inevitably arises when studying the Ricci flow with the tool of $\mathbb{F}$-convergence [Bam20a,Bam20b,Bam20c]. In this article, we shall present a systematic study of the noncollapsed $\mathbb{F}$-limit metric soliton, and show that, apart from the known results in [Bam20c], it satisfies many properties of smooth Ricci shrinkers. In particular, we show a quadratic lower bound for the scalar curvature, a local gap theorem, a global Sobolev inequality, and an optimal volume growth lower bound. |
| title | On noncollapsed $\mathbb{F}$-limit metric solitons |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2401.03387 |