Lectures on the Ricci Flow
Lectures on the Ricci Flow
复制标题
DOI：
10.1017/cbo9780511721465.013
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
P. Topping
中科院分区：
文献类型：
--
作者：
P. Topping
1.导论2.黎曼几何背景3.最大值原理4.抛物型偏微分方程解的存在性理论5.Ricci流的存在性理论6.作为梯度流的Ricci流7.黎曼流形和流的紧性8.Perelman的W熵泛函9.在Ricci流下的曲率收缩和保持曲率性质10.具有正Ricci曲率及以上的三种流形.
1. Introduction 2. Riemannian geometry background 3. The maximum principle 4. Comments on existence theory for parabolic PDE 5. Existence theory for the Ricci flow 6. Ricci flow as a gradient flow 7. Compactness of Riemannian manifolds and flows 8. Perelman's W entropy functional 9. Curvature pinching and preserved curvature properties under Ricci flow 10. Three-manifolds with positive Ricci curvature and beyond.