相关论文: The CR Paneitz Operator and the Stability of CR Pl…

Let $\Omega$ be a bounded strictly pseudoconvex domain in $C^2$ with a smooth, connected and compact boundary M and having a CR structure $J_0$ induced from $C^2$. Assume this CR structure has zero Webster torsion. Then if we deform the CR…

For CR structures in dimension three, the CR pluriharmonic functions are characterized by the vanishing of a third order operator. This third order operator, after composition with the divergence operator, gives the fourth order analogue of…

The nonnegativity of the CR Paneitz operator plays a crucial role in three-dimensional CR geometry. In this paper, we prove this nonnegativity for embeddable CR manifolds. This result and previous works give an affirmative solution of the…

The CR Paneitz operator is closely related to some important problems in CR geometry. In this paper, we consider this operator on a non-embeddable CR manifold. This operator is essentially self-adjoint and its spectrum is discrete except…

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…

Let $(X,T^{1,0}X)$ be a compact orientable embeddable three dimensional strongly pseudoconvex CR manifold and let ${\rm P\,}$ be the associated CR Paneitz operator. In this paper, we show that (I) ${\rm P\,}$ is self-adjoint and ${\rm P\,}$…

In this note, we mainly focus on the existence of pseudo-Einstein contact forms, an upper bound eigenvalue estimate for the CR Paneitz operator and its applications to the uniformization theorem for Sasakian space form in an embeddable…

In this article, we give a brief survey of recent developments on relations between global embeddability of a closed strictly pseudoconvex CR manifold and the CR Paneitz operator.

We introduce a fourth order CR invariant operator on pluriharmonic functions on a three-dimensional CR manifold, generalizing to the abstract setting the operator discovered by Branson, Fontana and Morpurgo. For a distinguished class of…

We develop the notion of renormalized energy in CR geometry, for maps from a strictly pseudoconvex pseudohermitian manifold to a Riemannian manifold. This energy is a CR invariant functional, whose critical points, which we call CR-harmonic…

We study the distribution kernel of a Toeplitz operator associated with a classical pseudodifferential operator on a compact, embeddable, strictly pseudoconvex CR manifold. The main result consists of a formula for the values at the…

We present a conformal deformation involving a fully nonlinear equation in dimension 4, starting with positive scalar curvature. Assuming a certain conformal invariant is positive, one may deform from positive scalar curvature to a stronger…

The critical CR GJMS operator on a strictly pseudoconvex CR manifold is a non-hypoelliptic CR invariant differential operator. We prove that, under the embeddability assumption, it is essentially self-adjoint and has closed range. Moreover,…

Let $M^{2n-1}$ be the smooth boundary of a bounded strongly pseudo-convex domain $\Omega$ in a complete Stein manifold $V^{2n}$. Then (1) For $n \ge 3$, $M^{2n-1}$ admits a pseudo-Eistein metric; (2) For $n \ge 2$, $M^{2n-1}$ admits a…

Using a bigraded differential complex depending on the CR and pseudohermitian structure, we give a characterization of three-dimensional strongly pseudoconvex pseudo-hermitian CR-manifolds isometrically immersed in Euclidean space…

A closed CR 3-manifold is said to have $C_{0}$-positive pseudohermitian curvature if $(W+C_{0}Tor)(X,X)>0$ for any $0\neq X\in T_{1,0}(M)$. We discover an obstruction for a closed CR 3-manifold to possess $C_{0}$-positive pseudohermitian…

In this paper we consider Riemannian manifolds $(M^n,g)$ of dimension $n \geq 5$, with semi-positive $Q$-curvature and non-negative scalar curvature. Under these assumptions we prove $(i)$ the Paneitz operator satisfies a strong maximum…

In this note, we affirm the partial answer to the long open Conjecture which states that any closed embeddable strictly pseudoconvex CR $3$-manifold admits a contact form $\theta $ with the vanishing CR $Q$-curvature. More precisely, we…

The purpose of this article is to study compactness of the complex Green operator on CR manifolds of hypersurface type. We introduce (CR-P_q), a potential theoretic condition on $(0,q)$-forms that generalizes Catlin's property (P_q) to CR…

In this paper, we investigate the geometry and classification of three-dimensional CR Yamabe solitons. In the compact case, we show that any 3-dimensional CR Yamabe soliton must have constant Tanaka-Webster scalar curvature; we also obtain…