39 citations · 95 across the 38 of their papers we have counts for
38 papers
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…
On minimizing surfaces of the CR invariant energy
Jih-Hsin Cheng, Hung-Lin Chiu, Paul Yang +1
We study a CR-invariant equation for vanishing surfaces in the 3-dimensional Heisenberg group. This is shown to be a hyperbolic equation. We prove the local uniqueness theore…
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 and a Grassmannian with a holomorphic li…
Heat kernel and local index theorem for open complex manifolds with -action
Jih-Hsin Cheng, Chin-Yu Hsiao, I-Hsun Tsai
For a complex manifold with -action, we define the -th Fourier-Dolbeault cohomology group and consider the -index on . By appl…
A characterization of homogeneous three-dimensional CR manifolds
Jih-Hsin Cheng, Andrea Malchiodi, Paul Yang
We characterize homogeneous three-dimensional CR manifolds, in particular Rossi spheres, as critical points of a certain energy functional that depends on the Webster curvature and…
On the variation of the Einstein-Hilbert action in pseudohermitian geometry
Claudio Afeltra, Jih-Hsin Cheng, Andrea Malchiodi +1
In this paper we compute the first and second variation of the normalized Einstein-Hilbert functional on CR manifolds. We characterize critical points as pseudo-Einstein structures…