Wei-Ting Kao

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math.DG2026

The Sharp Isoperimetric Inequality in the First Heisenberg Group

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

We prove the sharp horizontal isoperimetric inequality in the first Heisenberg group for all sets of finite horizontal perimeter and positive finite volume, with equality precisely…

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

A Reilly-Type Inequality for CR Dirac Operators on CR Manifolds and Applications

Jih-Hsin Cheng, Hung-Lin Chiu, Wei-Ting Kao

The first two authors derived the Weitzenböck-type Formula for a CR Dirac operator. In this paper, we apply the above-mentioned formula and follow the process as Riemannian case to…