Wei-Chun Chen

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math.DG2026

The Isoperimetric Inequality in Higher-Dimensional Heisenberg Groups

Wei-Chun Chen, Wei-Ting Kao, Chun-Kai Lien

We prove the sharp horizontal isoperimetric inequality in $H^{n}$ , $n \geq 2$ , with equality precisely for left translates and Heisenberg dilations of Pansu balls, up to Haar-nu…

math.DG2026

Quantitative Centre Rigidity under Riemannian Approximation in Heisenberg Groups

Wei-Chun Chen, Wei-Ting Kao, Chun-Kai Lien

For $n \geq 2$ , we prove a quantitative centre-rigidity estimate for bounded sets of finite Riemannian perimeter that are stationary and volume-constrained stable for normalized Riema…

math.DG2026

Stable Rigidity in the Heisenberg Groups

Wei-Chun Chen, Wei-Ting Kao, Chun-Kai Lien

For $n \geq 2$ , we prove that the $C^{2}$ boundary of a bounded nonempty open set in $H^{n}$ is volume-preserving stable if and only if it is a Pansu sphere up to left translation…

math.DG2026

The Jacobi Spectrum and Global Second Variation of Pansu Spheres

Wei-Chun Chen, Wei-Ting Kao, Chun-Kai Lien

For $n \geq 2$ , we establish second differentiability of horizontal perimeter for compact $C^{2}$ boundaries in $H^{n}$ and the continuous extension of their affine second variati…

math.DG2026

The Exact Comass Criterion for the Tsai--Wang Form

Wei-Chun Chen, Chun-Kai Lien

For a map $F : Ω \subset R^{n} \to R^{m}$ , let $Θ (F)$ be the $n$ -form on $Ω \times R^{m}$ introduced by Tsai and Wang [arXiv:2604.04336]. If $λ_{1}, \dots, λ_{r}$ are the…