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Autori principali: Chen, Jiaqi, Shan, Yufei, Ye, Yinghui
Natura: Preprint
Pubblicazione: 2025
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Accesso online:https://arxiv.org/abs/2505.23440
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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
id 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