Loading [MathJax]/extensions/MathZoom.js
We propose a definition for analytic torsion of the contact complex on contact manifolds. We show it coincides with Ray–Singer torsion on any -dimensional CR Seifert manifold equipped with a unitary representation. In this particular case we compute it and relate it to dynamical properties of the Reeb flow. In fact the whole spectral torsion function we consider may be interpreted on CR Seifert manifolds as a purely dynamical function through Selberg-like trace formulae, that hold also in variable...
We show that the local automorphism group of a minimal real-analytic CR manifold is a finite dimensional Lie group if (and only if) is holomorphically nondegenerate by constructing a jet parametrization.
We construct the CR invariant canonical contact form on scalar positive spherical CR manifold , which is the CR analogue of canonical metric on locally conformally flat manifold constructed by Habermann and Jost. We also construct another
canonical contact form on the Kleinian manifold , where is a convex cocompact subgroup of and is the discontinuity domain of . This contact form can be used to prove that is scalar positive (respectively, scalar negative, or scalar vanishing) if and...
We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for CR manifolds, that was first introduced by two of the authors, and the Hörmander’s bracket condition for real vector fields.Applications are given to prove the hypoellipticity of first order systems and second order partial differential operators.Finally we describe a class of compact homogeneous CR manifolds for which the distribution of vector fields satisfies...
We give a homotopy formula for the operator on a domain with (q+k)-concave boundary. As a consequence we show that the dimension of the -cohomology groups for some CR manifolds q-concave at infinity is finite.
There are only some exceptional CR dimensions and codimensions such that the geometries enjoy a discrete classification of the pointwise types of the homogeneous models. The cases of CR dimensions n and codimensions n 2 are among the very few possibilities of the so-called parabolic geometries. Indeed, the homogeneous model turns out to be PSU(n+1,n)/P with a suitable parabolic subgroup P. We study the geometric properties of such real (2n+n 2)-dimensional submanifolds in for all n > 1. In...
Given a Hörmander system on a domain we show that any subelliptic harmonic morphism from into a -dimensional riemannian manifold is a (smooth) subelliptic harmonic map (in the sense of J. Jost & C-J. Xu, [9]). Also is a submersion provided that and has rank . If (the Heisenberg group) and , where is the Lewy operator, then a smooth map is a subelliptic harmonic morphism if and only if is a harmonic morphism, where is the canonical circle bundle and is the Fefferman...
We give general sufficient conditions to guarantee that a given subgroup of the group of
diffeomorphisms of a smooth or real-analytic manifold has a compatible Lie group
structure. These results, together with recent work concerning jet parametrization and
complete systems for CR automorphisms, are then applied to determine when the global CR
automorphism group of a CR manifold is a Lie group in an appropriate topology.
We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface equation...
We present a large class of homogeneous 2-nondegenerate CR-manifolds , both of
hypersurface type and of arbitrarily high CR-codimension, with the following property: Every CR-equivalence
between domains , in extends to a global real-analytic CR-automorphism of . We show that this class contains -orbits in Hermitian symmetric spaces of compact type, where is a real form of the complex Lie group and has an open orbit that is a bounded symmetric domain of tube type.
We survey some recent results on holomorphic or formal mappings sending real submanifolds in complex space into each other. More specifically, the approximation and convergence properties of formal CR-mappings between real-analytic CR-submanifolds will be discussed, as well as the corresponding questions in the category of real-algebraic CR-submanifolds.
Le but de cet article est de montrer un résultat de prolongement d’un courant positif, défini en dehors d’un obstacle fermé, dont le est dominé par un courant positif fermé de masse localement finie. On étudie divers types d’obstacles : soit un ensemble fermé pluripolaire complet, soit l’ensemble des zéros d’une fonction strictement -convexe positive. Dans la troisième partie, sous des conditions sur la dimension de Hausdorff de l’obstacle, on démontre le prolongement d’un tel courant. On termine...
Let and be two compact strongly pseudoconvex CR manifolds of dimension which bound complex varieties and with only isolated normal singularities in and respectively. Let and be the singular sets of and respectively and is nonempty. If and the cardinality of is less than 2 times the cardinality of , then we prove that any non-constant CR morphism from to is necessarily a CR biholomorphism. On the other hand, let be a compact strongly pseudoconvex CR manifold of...
Let M be an open subset of a compact strongly pseudoconvex hypersurface {ρ = 0} defined by M = D × Cn-m ∩ {ρ = 0}, where 1 ≤ m ≤ n-2, D = {σ(z1, ..., zm) < 0} ⊂ Cm is strongly pseudoconvex in Cm. For ∂b closed (0, q) forms f on M, we prove the semi-global existence theorem for ∂b if 1 ≤ q ≤ n-m-2, or if q = n - m - 1 and f satisfies an additional “moment condition”. Most importantly, the solution operator satisfies Lp estimates for 1 ≤ p ≤ ∞ with p = 1 and ∞ included.
We study the tangential Cauchy-Riemann equations for -forms on quadratic manifolds. We discuss solvability for data in the Schwartz class and describe the range of the tangential Cauchy-Riemann operator in terms of the signatures of the scalar components of the Levi form.
For pseudocomplex abstract manifolds, the validity of the Poincaré Lemma for forms implies local embeddability in . The two properties are equivalent for hypersurfaces of real dimension . As a corollary we obtain a criterion for the non validity of the Poicaré Lemma for forms for a large class of abstract manifolds of codimension larger than one.
Currently displaying 1 –
18 of
18