Almost-Schur lemma

By Camillo De Lellis, P. Topping. 2010

56 citations recorded by the source corpus.

Schur’s lemma states that every Einstein manifold of dimension n ≥ 3 has constant scalar curvature. In this short note we ask to what extent the scalar curvature is constant if the traceless Ricci tensor is assumed to be small rather than identically zero. In particular, we provide an optimal L2 estimate under suitable assumptions and show that these assumptions cannot be removed.

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

View Paper: https://www.semanticscholar.org/paper/bc8df473f9b4e6210267e98091a85ca556389965

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. Guofang Wang
2. Chao Xia
3. Y. Yang
4. Julian Scheuer
5. M. Makowski
6. Yong Wei

In Astronomy and Astrophysics

1. Chao Xia
2. Guofang Wang

In Geometry and Topology

1. Chao Xia
2. Guofang Wang
3. Julian Scheuer
4. M. Makowski
5. Yong Wei

Citations in the corpus

• Isoperimetric type problems and Alexandrov-Fenchel type inequalities in the hyperbolic space (2013, background): “For the related work about the result of Cheng and Xu [11], see also [12], [17] and [21].”