具有2-Ricci曲率下界的3流形的体积比较与Ricci流
Volume comparison for 3-manifolds with 2-Ricci curvature lower bound and Ricci flow
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中文总结 AI 辅助
本文研究2-Ricci曲率下界3流形的体积比较，建立测地球面面积和球体积的单调性与刚性，并推导预紧性、Ricci流下曲率下界的保持及非负标量曲率的拓扑刚性。
中文摘要 AI 辅助
本文研究具有2-Ricci曲率下界的3流形的体积比较。我们建立了测地球面面积和球体积的单调性与刚性，并在共轭半径一致下界的条件下，推导了具有2-Ricci曲率下界的3流形的尖点Gromov-Hausdorff预紧性。我们还讨论了2-Ricci曲率下界沿Ricci流的几乎保持以及局部非塌缩传播。最后，我们指出了非负标量曲率的一个拓扑刚性结果。
英文摘要
In this note, we study volume comparison for 3-manifolds with 2-Ricci curvature lower bound. We establish monotonicity and rigidity for geodesic sphere area and ball volume, and derive the pointed Gromov-Hausdorff precompactness under a uniform lower bound on the conjugate radius for 3-manifolds with 2-Ricci curvature lower bound. We also discuss the almost preservation of 2-Ricci curvature lower bound and the local non-collapsing propagation along Ricci flow. Finally, we point out a topological rigidity result on nonnegative scalar curvature.
发表机构
- School of Science, Shenzhen Campus of Sun Yat-sen University（中山大学深圳校区理学院）
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