arXiv subjects

Guangrui Zhu

Publications and source records attributed to Guangrui Zhu.

3 recordsLinked to original sources

arXiv2026

A Llarull type theorem on complete non-compact manifolds

Let $3\leq n\leq7$, $2\leq k\leq n-1$, and $m=n-k-1$. We prove that a complete, connected, noncompact spin manifold $(M^n,g)$ with scalar curvature $R_M\geq k(k-1)$ is isometric to $\mathbb{S}^k\times\mathbb{T}^m_Λ\times\mathbb{R}$ if it admits a smooth proper map of nonzero degree to $\mathbb{S}^k\times\mathbb{T}^m\times\mathbb{R}$ whose spherical component is 1-Lipschitz. The flat torus in the conclusion is not necessarily isometric to the target torus.

math.DG↗

arXiv2026

Remarks on minimal hypersurfaces in shrinking gradient Ricci solitons

In this paper, we prove that any compact 2-sided smooth stable minimal hypersurface in a shrinking gradient Ricci soliton $(M^{n},g,f)$ with scalar curvature $R\geq(n-1)λ$ must have vanished second fundamental form and vanished normal Ricci curvature. For shrinking gradient Ricci solitons with scalar curvature $R\geq(n-1)λ$, the existence of an area-minimizing hypersurface would imply that $M$ is splitting.

math.DG↗

arXiv2025

A Weighted Llarull Type Theorem and its applications

This paper generalizes Llarull's classical scalar curvature rigidity theorem to the setting of weighted manifolds with P-scalar curvature. More precisely, we prove the refinement of Llarull's theorem for P-scalar curvature, which is similar to Listing's work \cite{listing2010scalar}. As an application, we establish a Llarull type theorem in the form of $\mathbb{S}^k\times\mathbb{T}^{n-k}$.

math.DG↗