Shengxuan Zhou

activity

20232026

4

-manifolds with nonnegative Ricci curvature and prescribed asymptotic cone

2 citations · 3 across the 6 of their papers we have counts for

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math.DG2024★ 2 cited

A family of $4$ -manifolds with nonnegative Ricci curvature and prescribed asymptotic cone

Shengxuan Zhou

In this paper, we show that for any finite subgroup $Γ < O (4)$ acting freely on $S^{3}$ , there exists a $4$ -dimensional complete Riemannian manifold $(M, g)$ with ${\rm Ric}_g…

math.DG2024

Examples of Ricci limit spaces with infinite holes

Shengxuan Zhou

Let $n \geq 3$ , $λ \in R$ , and $(X, h)$ be an $n$ -dimensional smooth complete Riemannian manifold with $Ric_{h} > λ$ . In this paper, we construct, for each given $ε > 0$ ,…

math.DG2024

New exotic examples of Ricci limit spaces

Xilun Li, Shengxuan Zhou

For any integers $m ⩾ n ⩾ 3$ , we construct a Ricci limit space $X_{m, n}$ such that for a fixed point, some tangent cones are $R^{m}$ and some are $\mathbb{R}^n…

math.DG2023★ 1 cited

On the Gromov-Hausdorff limits of Tori with Ricci conditions

Shengxuan Zhou

Let $n \geq 4$ . In this paper, we construct a sequence of smooth Riemannian metrics $g_{i}$ on $R^{n}$ such that: (1) $g_{i} = g_{Euc}$ outside the standard Euclidean unit…

A family of 4-manifolds with nonnegative Ricci curvature and prescribed asymptotic cone

Examples of Ricci limit spaces with infinite holes

New exotic examples of Ricci limit spaces

On the Gromov-Hausdorff limits of Tori with Ricci conditions

A family of $4$ -manifolds with nonnegative Ricci curvature and prescribed asymptotic cone