Rigidity of Poincaré-Einstein manifolds with flat Euclidean conformal infinity
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909531726938112 |
|---|---|
| author | Lee, Sanghoon Wang, Fang |
| author_facet | Lee, Sanghoon Wang, Fang |
| contents | In this paper, we prove a rigidity theorem for Poincaré-Einstein manifolds whose conformal infinity is a flat Euclidean space. The proof relies on analyzing the propagation of curvature tensors over the level sets of an adapted boundary defining function. Additionally, we provide examples of Poincaré-Einstein manifolds with non-compact conformal infinities. Furthermore, we draw analogies with Ricci-flat manifolds exhibiting Euclidean volume growth, particularly when the compactified metric has non-negative scalar curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06062 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity of Poincaré-Einstein manifolds with flat Euclidean conformal infinity Lee, Sanghoon Wang, Fang Differential Geometry 53C24, 53C25 In this paper, we prove a rigidity theorem for Poincaré-Einstein manifolds whose conformal infinity is a flat Euclidean space. The proof relies on analyzing the propagation of curvature tensors over the level sets of an adapted boundary defining function. Additionally, we provide examples of Poincaré-Einstein manifolds with non-compact conformal infinities. Furthermore, we draw analogies with Ricci-flat manifolds exhibiting Euclidean volume growth, particularly when the compactified metric has non-negative scalar curvature. |
| title | Rigidity of Poincaré-Einstein manifolds with flat Euclidean conformal infinity |
| topic | Differential Geometry 53C24, 53C25 |
| url | https://arxiv.org/abs/2503.06062 |