Recent developments on the Hamilton’s Ricci Flow

By Huaihuo Cao, B.-l. Chen, Xiaohua Zhu. 2007

111 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9872bb95b7e09464b2aa8d67ee2d2e8a4bb8136f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Brett Kotschwar
2. Michele Rimoldi
3. Lu Wang
4. A. G. Setti
5. S. Pigola
6. M. Rigoli
7. Ovidiu Munteanu
8. Jiaping Wang

In Astronomy and Astrophysics

1. Lu Wang
2. Brett Kotschwar
3. Michele Rimoldi
4. S. Pigola
5. A. G. Setti
6. Jiaping Wang
7. M. Rigoli
8. Zhuhong Zhang

In Geometry and Topology

1. Michele Rimoldi
2. Lu Wang
3. Brett Kotschwar
4. A. G. Setti
5. S. Pigola
6. M. Rigoli
7. Ovidiu Munteanu
8. Jiaping Wang

Citations in the corpus

• Geometric, topological and differentiable rigidity of submanifolds in space forms (2011, methodology): “Later some differentiable pinching theorems for Riemannian manifolds via Ricci flows were obtained by several authors [5, 8, 9, 17].”
• Rigidity of Complete Gradient Steady Ricci Solitons with Harmonic Weyl Curvature (2021, unknown): “In the shrinking case, classification results for gradient Ricci solitons have been obtained by many authors under various curvature conditions on the Weyl tensor, e.g., [7; 9; 10; 17; 20; 21; 24; 28; 29; 30; 31; 33; 35; 36], etc.”
• Geometry of shrinking Ricci solitons (2014, methodology): “The extra conditions were later removed through the effort of Naber [22], Ni and Wallach [23], and Cao, Chen and Zhu [3].”
• Rigidity of asymptotically conical shrinking gradient Ricci solitons (2013, result): “Hamilton [33] proved that the only complete nonflat twodimensional shrinking solitons are the standard round metrics on S2 and RP 2, and, with a combination of results from his later paper [34] and the work of Ivey [35], Perelman [47], Ni-Wallach [46], and Cao-ChenZhu [16], it follows that the only ”
• Ricci almost solitons (2010, background): “In this direction, we limit ourselves to quote the far-reaching [3] by H.”
• GRADIENT SHRINKING SOLITONS WITH VANISHING WEYL TENSOR (2008, methodology): “a local version of the Hamilton-Ivey pinching estimate due to Chen (Corollary 2.4 of [4]), Cao-Chen-Zhu [ 2 ] obtained the following complete classification (without any curvature bound assumption) on 3-dimensional complete gradient shrinking soliton”