Inverse mean curvature flow and Ricci-pinched three-manifolds
| Autor: | Huisken, Gerhard, Koerber, Thomas |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $(M,g)$ be a complete, connected, non-compact Riemannian three-manifold with non-negative Ricci curvature satisfying $Ric\geq\varepsilon\,\operatorname{tr}(Ric)\,g$ for some $\varepsilon>0$. In this note, we give a new proof based on inverse mean curvature flow that $(M,g)$ is either flat or has non-Euclidean volume growth. In conjunction with results of J. Lott and of M.-C. Lee and P. Topping, this gives an alternative proof of a conjecture of R. Hamilton recently proven by A. Deruelle, F. Schulze, and M. Simon using Ricci flow. Comment: Final version to appear in J. Reine Angew. Math |
| Databáze: | arXiv |
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