Back to Search
Start Over
A Note on Ricci-pinched three-manifolds
- Publication Year :
- 2024
-
Abstract
- Let $(M, g)$ be a complete, connected, non-compact Riemannian $3$-manifold. Suppose that $(M,g)$ satisfies the Ricci--pinching condition $\mathrm{Ric}\geq\varepsilon\mathrm{R} g$ for some $\varepsilon>0$, where $\mathrm{Ric}$ and $\mathrm{R}$ are the Ricci tensor and scalar curvature, respectively. In this short note, we give an alternative proof based on potential theory of the fact that if $(M,g)$ has Euclidean volume growth, then it is flat. Deruelle-Schulze-Simon and by Huisken-K\"{o}rber have already shown this result and together with the contributions by Lott and Lee-Topping led to a proof of the so-called Hamilton's pinching conjecture.
- Subjects :
- Mathematics - Differential Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2409.05078
- Document Type :
- Working Paper