On a sharp volume estimate for gradient Ricci solitons with scalar curvature bounded below

By S. Zhang. 2009

53 citations recorded by the source corpus.

In this note, we obtain a sharp volume estimate for complete gradient Ricci solitons with scalar curvature bounded below by a positive constant. Using Chen-Yokota’s argument we obtain a local lower bound estimate of the scalar curvature for the Ricci flow on complete manifolds. Consequently, one has a sharp estimate of the scalar curvature for expanding Ricci solitons; we also provide a direct (elliptic) proof of this sharp estimate. Moreover, if the scalar curvature attains its minimum value at some point, then the manifold is Einstein.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/553a9d857b377d796e4840258ae5f99af95495fc

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. Michele Rimoldi
2. Ovidiu Munteanu
3. Xu Cheng
4. A. G. Setti
5. Jiaping Wang
6. Detang Zhou
7. S. Pigola
8. M. Rigoli

In Geometry and Topology

1. Michele Rimoldi
2. Ovidiu Munteanu
3. Xu Cheng
4. Jiaping Wang
5. A. G. Setti
6. Detang Zhou
7. M. Rigoli
8. S. Pigola

Citations in the corpus

• Volume estimate about shrinkers (2011, methodology): “In [14], the author used the method in [4] to prove the result.”
• Analysis of weighted Laplacian and applications to Ricci solitons (2011, background): “On the other hand, by the maximum principle, it was proved in [24, 32] that (5.”
• Ricci almost solitons (2010, background): “The next result extends Theorem 3 in [27] to the case of almost solitons; see also [35].”