# Volume comparison theorem with respect to sigma-2 curvature

@inproceedings{Fang2021VolumeCT, title={Volume comparison theorem with respect to sigma-2 curvature}, author={Yi Fang and Yan Mary He and Jingyang Zhong}, year={2021} }

In this paper, we consider the volume comparison theorem related to σ2 curvature. We proved that if the σ2 curvature of sphere is greater than σ2 curvature of Einstein manifold with positive Ricci curvature, than we have the volume of sphere is less than the volume of the sphere with standard metrics.

## One Citation

### On the $$\sigma _2$$-curvature and volume of compact manifolds

- MathematicsAnnali di Matematica Pura ed Applicata (1923 -)
- 2022

. In this work we are interested in studying deformations of the σ 2 -curvature and the volume. For closed manifolds, we relate critical points of the total σ 2 -curvature functional to the σ 2…

## References

SHOWING 1-10 OF 12 REFERENCES

### The Penrose inequality in general relativity and volume comparison theorems involving scalar curvature (thesis)

- Mathematics
- 1997

In this thesis we describe how minimal surface techniques can be used to prove the Penrose inequality in general relativity for two classes of 3-manifolds. We also describe how a new volume…

### Deformations of Q-curvature I

- Mathematics
- 2015

In this article, we investigate deformation problems of Q-curvature on closed Riemannian manifolds. One of the most crucial notions we use is the Q-singular space, which was introduced by…

### On scalar curvature rigidity of vacuum static spaces

- Mathematics
- 2014

In this paper we extend the local scalar curvature rigidity result in Brendle and Marques (J Differ Geom 88:379–394, 2011) to a small domain on general vacuum static spaces, which confirms the…

### Certain conditions for a Riemannian manifold to be isometric with a sphere

- Mathematics
- 1962

Introduction. In this paper, by a Riemannian manifold we always mean a connected $C^{\infty}-$ manifold of dimension $n(\geqq 2)$ with a positive definite $C^{\infty}$ -Riemannian metric. A…

### The manifold of Riemannian metrics

- Materials Science
- 1970

A cold setting refractory composition comprises a water-soluble aluminum phosphate binding agent, refractory filler and, as setting agent, magnesia of low reactivity.

### Volume Comparison of Conformally Compact Manifolds with Scalar Curvature R ≥ −n (n − 1)

- Mathematics
- 2016

In this paper, we use the normalized Ricci–DeTurk flow to prove a stability result for strictly stable conformally compact Einstein manifolds. As an application, we show a local volume comparison of…

### Variational theory for the total scalar curvature functional for riemannian metrics and related topics

- Mathematics
- 1989

### Ebin, The manifold of Riemannian metrics

- Proc. Sympos. Pure Math., Vol. XV, Berkeley, Calif.,
- 1968