arXiv subjects

Yufei Shan

Publications and source records attributed to Yufei Shan.

2 recordsLinked to original sources

arXiv2025

The volume comparison of symmetric spaces of non-compact type of rank 1

Motivated by Schoen's conjecture on the volume functional for closed hyperbolic manifolds, we generalize the volume comparison theorem of Hu, Ji, and Shi and establish a volume comparison theorem for rank 1 symmetric spaces of non-compact type under a scalar curvature condition. Furthermore, we prove a rigidity result. Our proof uses the normalized Ricci--DeTurck flow to analyze the asymptotic behavior of the volume functional and to derive monotonicity properties. This extends the classical volume comparison framework to symmetric spaces of non-compact type.

math.DG↗

arXiv2025

Comparison of total $\sigma_k$-curvature

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 $\sigma_l$-curvature with respect to $\sigma_k$-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.

math.DG↗