Related papers: CR $Q$-curvature and CR pluriharmonic functions
In this note, we will present global equisingular approximations of quasi-plurisubharmonic functions with stable analytic pluripolar sets on compact complex manifolds.
We consider the constant Q-curvature metric problem in the given conformal class on conic 4-manifolds and study related differential equations.
In this paper we show some results on homogeneous CR manifolds, proved by introducing their associated CR algebras. In particular, we give different notions of nondegeneracy (generalizing the usual notion for the Levi form) which correspond…
In this paper, we obtain the isoperimetric inequality on conformally flat manifold with finite total $Q$-curvature. This is a higher dimensional analogue of Li and Tam's result \cite{L-T} on surfaces with finite total Gaussian curvature.…
We prove that every compact, pseudoconvex, orientable, CR manifold of $\C^n$, bounds a complex manifold in the $C^\infty$ sense. In particular, the tangential Cauchy-Riemann system has closed range.
It is proved that if there exists a positive and continuous function $f$ on an $n$-dimensional complex manifold $X$, $q$-convex with corners outside a compact set $K\subset X$ and which exhausts $X$ from below, then…
In this article, we consider a complete, non-compact almost Hermitian manifold whose curvature is asymptotic to that of the complex hyperbolic plane. Under natural geometric conditions, we show that such a manifold arises as the interior of…
Motivated by the Shilov boundaries of bounded symmetric domains we consider arbitrary CR-quadrics in a complex linear space (of finite dimension) that have a certain symmetry property. For these the non-affine local CR-automorphisms have a…
We use the CR geometry of the standard hyperquadric in complex projective three-space to give a detailed twistor description of conformal foliations in Euclidean three-space.
For a smooth strictly pseudoconvex hypersurface in a complex manifold, we give a necessary and sufficient condition for being CR-diffeomorphic to a real-analytic CR manifold. Our condition amounts to a holomorphic extension property for the…
In this note, we prove that the CR manifold which is induced from the canonical parabolic geometry of a quaternionic contact (qc) manifold via a Fefferman-type construction is equivalent to the CR twistor space of the qc manifold defined by…
Let M be a smooth locally embeddable CR manifold, having some CR dimension m and some CR codimension d. We find an improved local geometric condition on M which guarantees, at a point p on M, that germs of CR distributions are smooth…
In this paper we prove that for an almost complex orbifold, its virtual orbifold cohomology [math.AT/0606573] is isomorphic as algebras to the Chen-Ruan orbifold cohomology of its cotangent orbifold.
The objet of this paper is the study of variations of a functional whose integrant is the $\sigma_u$-curvature of closed submanifolds of arbitrary codimension in Riemannian manifolds.
In this paper, by searching the relation between the radial part of Higgs harmonic oscillator in the two-dimensional curved space and the generalized CRS harmonic oscillator model, we can find a series of quasi-exact models in…
Let X be a CW complex with a continuous action of a topological group G. We show that if X is equivariantly formal for singular cohomology with coefficients in a field, then so are all symmetric products of X and in fact all its…
We classify all compact simply connected homogeneous CR manifolds $M$ of codimension one and with non-degenerate Levi form up to CR equivalence. The classification is based on our previous results and on a description of the maximal…
In this paper, we establish a $q$-integral formula by using the orthogonality relation, and also provide a new proof of the $q$-orthogonality relation for the continuous $q$-ultraspherical polynomials. A new $q$-beta integral with five…
We introduce a cyclotomic representation for finite $q$-hypergeometric series and $q$-deformed amplitudes that separates algebraic structure from evaluation. By expressing each summand in a sparse exponent basis over irreducible cyclotomic…
A complex flag manifold F= G /Q decomposes into finitely many real orbits under the action of a real form of G. Their embedding into F define on them CR manifold structures. We characterize the closed real orbits which are finitely…