Strong uniqueness and rectifiability of generalized cylindrical singularities in Ricci flow
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917503304728576 |
|---|---|
| author | Fang, Hanbing Li, Yu |
| author_facet | Fang, Hanbing Li, Yu |
| contents | In this paper, we extend the results of \cite{fang2025strong, fang2025singular} to generalized cylinders. More precisely, we establish a Lojasiewicz inequality for the pointed $\mathcal{W}$-entropy in Ricci flow under the assumption that the geometry near the base point is close to a generalized cylinder $\mathbb{R}^k \times N^{n-k}$, where $N$ is an Einstein manifold with obstruction of order three satisfying a suitable spectral condition. As an application, we prove the strong uniqueness of generalized cylindrical tangent flows. Furthermore, we show that the subset $\mathcal{S}^k_{\mathrm{qc}}(N)\subset \mathcal{S}^k$, consisting of points at which some tangent flow is given by $\mathbb{R}^k \times N^{n-k}$ or its quotient, is horizontally parabolic $k$-rectifiable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17001 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strong uniqueness and rectifiability of generalized cylindrical singularities in Ricci flow Fang, Hanbing Li, Yu Differential Geometry In this paper, we extend the results of \cite{fang2025strong, fang2025singular} to generalized cylinders. More precisely, we establish a Lojasiewicz inequality for the pointed $\mathcal{W}$-entropy in Ricci flow under the assumption that the geometry near the base point is close to a generalized cylinder $\mathbb{R}^k \times N^{n-k}$, where $N$ is an Einstein manifold with obstruction of order three satisfying a suitable spectral condition. As an application, we prove the strong uniqueness of generalized cylindrical tangent flows. Furthermore, we show that the subset $\mathcal{S}^k_{\mathrm{qc}}(N)\subset \mathcal{S}^k$, consisting of points at which some tangent flow is given by $\mathbb{R}^k \times N^{n-k}$ or its quotient, is horizontally parabolic $k$-rectifiable. |
| title | Strong uniqueness and rectifiability of generalized cylindrical singularities in Ricci flow |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.17001 |