Related papers: Kohn-Rossi Cohomology and its application to the C…

Let $X$ be a compact connected strongly pseudoconvex $CR$ manifold of real dimension $2n-1$ in $\mathbb{C}^{N}$. It has been an interesting question to find an intrinsic smoothness criteria for the complex Plateau problem. For $n\ge 3$ and…

Let $X$ be a compact connected strongly pseudoconvex $CR$ manifold of real dimension $2n-1$ in $\mathbb{C}^{N}$. For $n\ge 3$, Yau solved the complex Plateau problem of hypersurface type by checking a bunch of Kohn-Rossi cohomology groups…

Building on work of Du, Gao, and Yau, we give a characterization of smooth solutions, up to normalization, of the complex Plateau problem for strongly pseudoconvex Calabi--Yau CR manifolds of dimension $2n-1 \ge 5$ and in the hypersurface…

The ``complex Plateau problem'' (or boundary problem) in a complexe manifold X is the problem of characterizing the real submanifolds $\Gamma$ of X which are boundaries of analytic sub-varieties of $X \backslash \Gamma$. Our principal…

We give a new CR invariant treatment of the bigraded Rumin complex and related cohomology groups via differential forms. A key benefit is the identification of balanced $A_\infty$-structures on the Rumin and bigraded Rumin complexes. We…

We solve the Levi-flat Plateau problem in the following case. Let $M \subset {\mathbb C}^{n+1}$, $n \geq 2$, be a connected compact real-analytic codimension-two submanifold with only nondegenerate CR singularities. Suppose $M$ is a…

Let $M$ be a compact, pseudoconvex-oriented, $(2n+1)$-dimensional, abstract CR manifold of hypersurface type, $n\geq 2$. We prove the following: (i) If $M$ admits a strictly CR-plurisubharmonic function on $(0,q_0)$-forms, then the complex…

This paper continues the previous studies in two papers of Huang-Yin [HY3-4] on the flattening problem of a CR singular point of real codimension two sitting in a submanifold in ${\mathbb C}^{n+1}$ with $n+1\ge 3$, whose CR points are…

Let M of real dimension 2n-1 be a compact, orientable, weakly pseudoconvex manifold of dimension at least five, embedded in C^N (n less than or equal to N), of codimension one or more in C^N, and endowed with the induced CR structure. We…

A joint generalization of real smooth as well of complex manifolds are the Cauchy-Riemann manifolds. The main objective of the paper is to inroduce a class of symmetric CR manifolds containing both classes of Riemannian and Hermitian…

We consider a formally integrable, strictly pseudoconvex CR manifold $M$ of hypersurface type, of dimension $2n-1\geq7$. Local CR, i.e. holomorphic, embeddings of $M$ are known to exist from the works of Kuranishi and Akahori. We address…

The first part of this paper considers higher order CR invariants of three dimensional hypersurfaces of finite type. Using a full normal form we give a complete characterization of hypersurfaces with trivial local automorphism group, and…

We study regularity properties of CR maps in positive codimension valued in pseudoconvex manifolds which carry a nontrivial Levi foliation. We introduce an invariant which can be used to deduce that any sufficiently regular CR map from a…

We study compactness and noncompactness phenomena for the CR Yamabe equation on compact strictly pseudoconvex CR manifolds. First, in dimension five we establish uniform \emph{a priori} estimates for families of positive solutions of…

Searching normal forms for real analytic submanifolds of C^n involves convergence problems. In 1983, J.K. Moser and S.M. Webster provided examples of real analytic surfaces in C^2 having an isolated hyperbolic (in the sense of E. Bishop)…

Let $(M,Q)$ be a compact, three dimensional manifold of strictly negative sectional curvature. Let $(\Sigma,P)$ be a compact, orientable surface of hyperbolic type (i.e. of genus at least two). Let $\theta:\pi_1(\Sigma,P)\to\pi_1(M,Q)$ be a…

We compute a recently introduced geometric invariant of stricly pseudoconvex CR 3-manifolds for certain circle invariant spherical CR structures on Seifert manifolds. We give applications to the problem of filling the CR manifold by a…

We show how to find a complete set of necessary and sufficient conditions that solve the fixed-parameter local congruence problem of immersions in $G$-spaces, whether homogeneous or not, provided that a certain $k^{\rm th}$ order jet bundle…

In our earlier work \cite{KZ}, we introduced an analytic regularizability theory for smooth strictly pseudoconvex hypersurfaces in complex space. That is, we found a necessary and sufficient condition for a hypersurface to be CR-equivalent…

We define an invariant, which we call surface-complexity, of compact 3-manifolds by means of Dehn surfaces. The surface-complexity is a natural number measuring how much the manifold is complicated. We prove that it fulfils interesting…