Author

Jun-Qi Lai

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Preprint Sep 2026

Construction of compact embedded ${\lambda}$-hypersurfaces via isoparametric hypersurfaces

We construct closed embedded ${\lambda}$-hypersurfaces in ${\mathbb{R}^{n+1}}$ of topological type ${S^1\times M}$ for any ${\lambda \ge 0}$, where ${M\subset\mathbb{S}^n}$ is an isoparametric hypersurface with equal principal curvature multiplicities. This extends previous results of Angenent, McGrath, and Riedler (fo...

Jun-Qi Lai, Guo-Xin Wei · 0 citations

Preprint Sep 2026

Singular Rotational Self-Similar Tori for Odd $\sigma_k$-Curvature Flows

For every pair of integers $3\leq k<n$ with $k$ odd, we construct a compact embedded rotational torus in $\mathbb{R}^{n+1}$ whose homothetic dilations satisfy the unnormalised $\sigma_k$-curvature flow in a Sobolev almost-everywhere sense. Its profile curve has H\"older regularity $C^{1,1/k}$ and Sobolev regularity $W^...

Hao-Xuan Cheng, Jun-Qi Lai, Guo-Xin Wei · 0 citations