Geometry of Complete Gradient Shrinking Ricci Solitons

By Huaihuo Cao. 2009

61 citations recorded by the source corpus.

We survey some of the recent progress on complete gradient shrinking Ricci solitons, including the classifications in dimension three and asymptotic behavior of potential functions as well as volume growths of geodesic balls in higher dimensions. This article is written for the conference proceedings dedicated to Yau's 60th birthday.

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

View Paper: https://www.semanticscholar.org/paper/f930e69d51214c5e2f68689c4f815b8e6ae753b7

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. Lu Wang
2. Xu Cheng
3. Brett Kotschwar
4. Ovidiu Munteanu
5. Detang Zhou
6. N. Šešum
7. Robert Haslhofer
8. Huaihuo Cao

In Astronomy and Astrophysics

1. Lu Wang
2. Ovidiu Munteanu
3. Brett Kotschwar
4. N. Šešum
5. Detang Zhou
6. Xu Cheng
7. Huaihuo Cao
8. Qiang Chen

In Geometry and Topology

1. Lu Wang
2. Xu Cheng
3. Ovidiu Munteanu
4. Detang Zhou
5. Brett Kotschwar
6. N. Šešum
7. Huaihuo Cao
8. Jiaping Wang

Citations in the corpus

• Rigidity of asymptotically conical shrinking gradient Ricci solitons (2013, methodology): “We refer the reader to the two surveys [13], [14] of Cao for a detailed picture of the current state of the art.”
• Volume estimate about shrinkers (2011, background): “5 [1]), we can choose a new f , still denoted by f , such that C0 is equal to the infimum of R.”
• On Gradient Ricci Solitons (2009, background): “cci soliton (M,g) is infinite. More precisely, there are constants c,r0 > 0 so that for any r > r0, Vol(Bp(r)) ≥ c ·r. We note that it is known that shrinking Ricci solitons have infinite volume ([3]), in fact there is a constant c > 0 so that Vol(Bp(r)) ≥ clnr, where c depends on p but is in”