Chun-Kai Lien

collaborators

7 papers

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

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…

math.DG2025

Bernstein Theorems for Calibrated Submanifolds in $R^{7}$ and $R^{8}$

Chun-Kai Lien, Chung-Jun Tsai

This paper explores the Bernstein problem of smooth maps $f : R^{4} \to R^{3}$ whose graphs form coassociative submanifolds in $R^{7}$ . We establish a condition,…

The Sharp Isoperimetric Inequality in the First Heisenberg Group

The Isoperimetric Inequality in Higher-Dimensional Heisenberg Groups

Quantitative Centre Rigidity under Riemannian Approximation in Heisenberg Groups

Stable Rigidity in the Heisenberg Groups

The Jacobi Spectrum and Global Second Variation of Pansu Spheres

The Exact Comass Criterion for the Tsai--Wang Form

Bernstein Theorems for Calibrated Submanifolds in R7 and R8

Bernstein Theorems for Calibrated Submanifolds in $R^{7}$ and $R^{8}$