Jih-Hsin Cheng

collaborators

4 papers

math.DG2026

Positive mass theorem and the Yamabe equation on CR manifolds

Jih-Hsin Cheng

Our goal is to survey the development of positive mass theorem and the Yamabe equation on CR manifolds in recent years. We introduce the notion of the mass in several complex varia…

math.DG2026

Spectral bundles on Abelian varieties, complex projective spaces and Grassmannians

Ching-Hao Chang, Jih-Hsin Cheng, I-Hsun Tsai

In this paper we study the spectral analysis of Bochner-Kodaira Laplacians on an Abelian variety, complex projective space $P^{n}$ and a Grassmannian with a holomorphic li…

math.DG2025

On minimizing surfaces of the CR invariant energy $E_{1}$

Jih-Hsin Cheng, Hung-Lin Chiu, Paul Yang +1

We study a CR-invariant equation for vanishing $E_{1}$ surfaces in the 3-dimensional Heisenberg group. This is shown to be a hyperbolic equation. We prove the local uniqueness theore…

math.DG2025

Heat kernel and local index theorem for open complex manifolds with $C^{*}$ -action

Jih-Hsin Cheng, Chin-Yu Hsiao, I-Hsun Tsai

For a complex manifold $I^£$ with $C^{*}$ -action, we define the $m$ -th $C^{*}$ Fourier-Dolbeault cohomology group and consider the $m$ -index on $I^£$ . By ap…

Positive mass theorem and the Yamabe equation on CR manifolds

Spectral bundles on Abelian varieties, complex projective spaces and Grassmannians

On minimizing surfaces of the CR invariant energy E1​

Heat kernel and local index theorem for open complex manifolds with C∗-action

On minimizing surfaces of the CR invariant energy $E_{1}$

Heat kernel and local index theorem for open complex manifolds with $C^{*}$ -action