Hung-Lin Chiu

Embeddability for 3-dimensional Cauchy–Riemann manifolds and CR Yamabe invariants

Let M^3 be a closed CR 3-manifold. In this paper we derive a Bochner formula for the Kohn Laplacian in which the pseudo-hermitian torsion plays no role. By means of this formula we show that the non-zero eigenvalues of the Kohn Laplacian are bounded below by a positive constant provided the CR Paneitz operator is non-negative and the Webster curvature is positive. Our lower bound for the non-zero eigenvalues is sharp and is attained on S^3. A consequence of our lower bound is that all compact CR 3-manifolds with non-negative CR Paneitz operator and positive CR Yamabe constant are embeddable. Non-negativity of the CR Paneitz operator and positivity of the CR Yamabe constant are both CR invariant conditions and do not depend on conformal changes of the contact form. In addition we show that under the sufficient conditions above for embeddability, the embedding is stable in the sense of Burns and Epstein. We also show that for the Rossi example for non-embedability, the CR Paneitz operator is negative. For CR structures close to the standard structure on

Uniformization of spherical CR manifolds

S^3

The Li-Yau-Hamilton inequality for Yamabe flow on a closed CR 3-manifold

we show the CR Paneitz operator is positive on the space of pluriharmonic functions with respect to the standard CR structure on

Connected Sum of Spherical CR Manifolds with Positive CR Yamabe Constant

S^3

Nonnegativity of CR Paneitz Operator and Its Application to the CR Obata’s Theorem

.

On the CR analogue of Obata’s theorem in a pseudohermitian 3-manifold

Let

ON THE ESTIMATE OF THE FIRST EIGENVALUE OF A SUBLAPLACIAN ON A PSEUDOHERMITIAN 3-MANIFOLD

M

A fourth order curvature flow on a CR 3-manifold

be a closed (compact with no boundary) spherical

EMBEDDED THREE-DIMENSIONAL CR MANIFOLDS AND THE NON-NEGATIVITY OF PANEITZ OPERATORS

CR

The fundamental theorem for hypersurfaces in Heisenberg groups

manifold of dimension