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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.23440 |
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Table of 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.