Comparison of total $σ_k$-curvature
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908865757446144 |
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| author | Chen, Jiaqi Shan, Yufei Ye, Yinghui |
| author_facet | Chen, Jiaqi Shan, Yufei Ye, Yinghui |
| contents | Volume comparison theorem is a type of fundamental results in Riemannian geometry. In this article, we extend the volume comparison result in \cite{Besse2008} to the comparison of total $σ_l$-curvature with respect to $σ_k$-curvature ($l<k$). In particular, we prove the comparison holds for metrics close to strictly stable positive Einstein metric with $l<\frac{n}{2}$. As for negative Einstein metrics, we prove a similar comparison result provided certain assumptions on sectional curvature holds for the manifold. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_23440 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Comparison of total $σ_k$-curvature Chen, Jiaqi Shan, Yufei Ye, Yinghui Differential Geometry Volume comparison theorem is a type of fundamental results in Riemannian geometry. In this article, we extend the volume comparison result in \cite{Besse2008} to the comparison of total $σ_l$-curvature with respect to $σ_k$-curvature ($l<k$). In particular, we prove the comparison holds for metrics close to strictly stable positive Einstein metric with $l<\frac{n}{2}$. As for negative Einstein metrics, we prove a similar comparison result provided certain assumptions on sectional curvature holds for the manifold. |
| title | Comparison of total $σ_k$-curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2505.23440 |