Shengxuan Zhou

activity

20242026

collaborators

5 papers

math.AP2026

Regularity of Second-Order Elliptic PDEs in Spectral Barron Spaces

Ziang Chen, Liqiang Huang, Mengxuan Yang +1

We establish a regularity theorem for second-order elliptic PDEs on $R^{d}$ in spectral Barron spaces. Under mild ellipticity and smallness assumptions, the solution gains…

math.NT2026

Quantitativity on the number of rational points in the Mordell conjecture

Jiawei Yu, Xinyi Yuan, Shengxuan Zhou

In this paper, we prove an explicit upper bound on the number of rational points on a smooth projective curve of genus at least two over a number field. This gives explicit constan…

math.DG2025

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…

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.DG2024

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 $I^ < O (4)$ acting freely on $S^{3}$ , there exists a $4$ -dimensional complete Riemannian manifold $(M, g)$ with ${\rm Ric}_…

Regularity of Second-Order Elliptic PDEs in Spectral Barron Spaces

Quantitativity on the number of rational points in the Mordell conjecture

On the Gromov-Hausdorff limits of Tori with Ricci conditions

New exotic examples of Ricci limit spaces

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

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