Nonlinear potential theory and Ricci-pinched 3-manifolds
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911435813027840 |
|---|---|
| author | Benatti, Luca Quirós, Ariadna León Oronzio, Francesca Pluda, Alessandra |
| author_facet | Benatti, Luca Quirós, Ariadna León Oronzio, Francesca Pluda, Alessandra |
| contents | In this paper, we focus on Hamilton's pinching conjecture formulated in Hamilton's paper "Three-manifolds with positive Ricci curvature". Let $(M, g)$ be a complete, connected, noncompact Riemannian $3$-manifold satisfying the Ricci-pinching condition. Then, it is flat. Here, we give an alternative proof, based on nonlinear potential theory, under the extra hypothesis of superquadratic volume growth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20281 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear potential theory and Ricci-pinched 3-manifolds Benatti, Luca Quirós, Ariadna León Oronzio, Francesca Pluda, Alessandra Differential Geometry In this paper, we focus on Hamilton's pinching conjecture formulated in Hamilton's paper "Three-manifolds with positive Ricci curvature". Let $(M, g)$ be a complete, connected, noncompact Riemannian $3$-manifold satisfying the Ricci-pinching condition. Then, it is flat. Here, we give an alternative proof, based on nonlinear potential theory, under the extra hypothesis of superquadratic volume growth. |
| title | Nonlinear potential theory and Ricci-pinched 3-manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2412.20281 |