Junqi Lai

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20242026

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math.DG2026

Construction of compact embedded $λ$ -hypersurfaces via isoparametric hypersurfaces

Lai Junqi, Wei Guoxin

We construct closed embedded $λ$ -hypersurfaces in $R^{n + 1}$ of topological type $S^{1} \times M$ for any $λ \geq 0$ , where $M \subset S^{n}$ is an isoparametric hy…

math.DG2026

Singular Rotational Self-Similar Tori for Odd $σ_{k}$ -Curvature Flows

Haoxuan Cheng, Junqi Lai, Guoxin Wei

For every pair of integers $3 \leq k < n$ with $k$ odd, we construct a compact embedded rotational torus in $R^{n + 1}$ whose homothetic dilations satisfy the unnormalised $σ_k…

math.DG2026

Examples of compact embedded mean convex $λ$ -hypersurfaces

Qing-Ming Cheng, Junqi Lai, Guoxin Wei

There is a well-known conjecture asserts that the round sphere should be the only compact embedded self-shrinker (i.e. $0$ -hypersurface) which is diffeomorphic to a sphere. S. Bren…

math.DG2026

Minimal hypersurfaces in spheres generated by isoparametric foliations

Junqi Lai, Guoxin Wei

We investigate the existence of minimal hypersurfaces in $S^{n + 1}$ that are generated by the isoparametric foliation of a subsphere $S^{n}$ . By considering a genera…

math.DG2025

Embedded constant mean curvature hypertori in the $2 n$ -sphere

Junqi Lai, Guoxin Wei

Brendle proved Lawson conjecture about minimal embedded torus in the round three-dimensional sphere. Carlotto and Schulz constructed a minimal embedded three-dimensional hypertorus…

math.DG2024

Embedded cylindrical and doughnut-shaped $λ$ -hypersurfaces

Qing-Ming Cheng, Junqi Lai, Guoxin Wei

In the paper, we construct, for $λ > 0$ , complete embedded and non-convex $λ$ -hypersurfaces, which are diffeomorphic to a cylinder. Hence, one can not expect that $λ$ -hypersurfaces s…

Construction of compact embedded λ-hypersurfaces via isoparametric hypersurfaces

Singular Rotational Self-Similar Tori for Odd σk​-Curvature Flows

Examples of compact embedded mean convex λ-hypersurfaces

Minimal hypersurfaces in spheres generated by isoparametric foliations

Embedded constant mean curvature hypertori in the 2n-sphere

Embedded cylindrical and doughnut-shaped λ-hypersurfaces

Construction of compact embedded $λ$ -hypersurfaces via isoparametric hypersurfaces

Singular Rotational Self-Similar Tori for Odd $σ_{k}$ -Curvature Flows

Examples of compact embedded mean convex $λ$ -hypersurfaces

Embedded constant mean curvature hypertori in the $2 n$ -sphere

Embedded cylindrical and doughnut-shaped $λ$ -hypersurfaces