AI 中文总结
研究非负标量曲率下可缩三维流形及柄体内部拓扑刚性，通过证明可缩三维流形与\(\mathbb{R}^3\)微分同胚等，回答了王和格罗莫夫的两个开放性问题。
AI 中文摘要
我们证明了一个允许具有非负标量曲率的完备黎曼度量的可缩三维流形与\(\mathbb{R}^3\)微分同胚。还证明了，如果亏格为\(\gamma\)的紧致柄体的内部\(M_\gamma\)允许这样的度量，那么\(\gamma\leq1\)。这分别回答了王和格罗莫夫提出的两个开放性问题。
英文摘要
We prove that a contractible $3$-manifold admitting a complete Riemannian metric of nonnegative scalar curvature is diffeomorphic to $\R^3$. We also prove that, if the interior $M_γ$ of a compact handlebody of genus $γ$ admits such a metric, then $γ\leq1$. This answers two open questions posed by Wang and Gromov, respectively.
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