Integrable Deformations and Stability of the Ricci Flow
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914480327229440 |
|---|---|
| author | Stolarski, Maxwell Waldron, Alex |
| author_facet | Stolarski, Maxwell Waldron, Alex |
| contents | We provide a comparatively simple proof of the dynamical stability of Ricci flow near a linearly stable Ricci-flat ALE metric with integrable deformations. Our proof relies on the equivalence between integrability and an "almost-orthogonality" property of the Ricci-DeTurck tensor, allowing us to analyze the latter directly. We obtain our main results in weighted Holder spaces and then show how to recover the $L^p$-stability theorems of Deruelle-Kroncke and Kroncke-Petersen. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15198 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Integrable Deformations and Stability of the Ricci Flow Stolarski, Maxwell Waldron, Alex Differential Geometry Analysis of PDEs We provide a comparatively simple proof of the dynamical stability of Ricci flow near a linearly stable Ricci-flat ALE metric with integrable deformations. Our proof relies on the equivalence between integrability and an "almost-orthogonality" property of the Ricci-DeTurck tensor, allowing us to analyze the latter directly. We obtain our main results in weighted Holder spaces and then show how to recover the $L^p$-stability theorems of Deruelle-Kroncke and Kroncke-Petersen. |
| title | Integrable Deformations and Stability of the Ricci Flow |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2604.15198 |