scholarly journals Analytic discs attached to a generating CR-manifold

1995 ◽  
Vol 33 (2) ◽  
pp. 217-248 ◽  
Author(s):  
Miran Černe
Keyword(s):  
Cr Manifold ◽  
Analytic Discs

Polynomial hulls and analytic discs

2017 ◽  
Vol 145 (10) ◽  
pp. 4443-4448
Author(s):  
Egmont Porten
Keyword(s):  
Analytic Discs ◽  
Polynomial Hulls

scholarly journals Directions of Analytic Discs Attached to Generic Manifolds of Finite Type

1994 ◽  
Vol 125 (1) ◽  
pp. 149-171
Author(s):  
M.S. Baouendi ◽  
L.P. Rothschild
Keyword(s):  
Finite Type ◽  
Analytic Discs

scholarly journals Regularity of CR mappings of abstract CR structures

2019 ◽  
Vol 31 (01) ◽  
pp. 2050009
Author(s):  
Bernhard Lamel ◽  
Nordine Mir
Keyword(s):  
Euclidean Space ◽  
Infinite Order ◽  
Extension Property ◽  
Cr Manifold ◽  
Generic Point ◽  
Cr Mappings ◽  
Complex Euclidean Space ◽  
Cr Structures ◽  
Cr Map ◽  
Regularity Results

We study the [Formula: see text] regularity problem for CR maps from an abstract CR manifold [Formula: see text] into some complex Euclidean space [Formula: see text]. We show that if [Formula: see text] satisfies a certain condition called the microlocal extension property, then any [Formula: see text]-smooth CR map [Formula: see text], for some integer [Formula: see text], which is nowhere [Formula: see text]-smooth on some open subset [Formula: see text] of [Formula: see text], has the following property: for a generic point [Formula: see text] of [Formula: see text], there must exist a formal complex subvariety through [Formula: see text], tangent to [Formula: see text] to infinite order, and depending in a [Formula: see text] and CR manner on [Formula: see text]. As a consequence, we obtain several [Formula: see text] regularity results generalizing earlier ones by Berhanu–Xiao and the authors (in the embedded case).

RESULTS RELATED TO PRESCRIBING PSEUDO-HERMITIAN SCALAR CURVATURE

2013 ◽  
Vol 24 (03) ◽  
pp. 1350020 ◽  
Author(s):  
PAK TUNG HO
Keyword(s):  
Scalar Curvature ◽  
Smooth Function ◽  
The Other ◽  
Cr Manifold ◽  
Geometric Flow ◽  
Yamabe Invariant ◽  
Uniqueness Results ◽  
Other Hand

In this paper, we consider the problem of prescribing pseudo-Hermitian scalar curvature on a compact strictly pseudoconvex CR manifold M. Using geometric flow, we prove that for any negative smooth function f we can prescribe the pseudo-Hermitian scalar curvature to be f, provided that dim M = 3 and the CR Yamabe invariant of M is negative. On the other hand, we establish some uniqueness and non-uniqueness results on prescribing pseudo-Hermitian scalar curvature.

Topology of Gleason Parts in Maximal Ideal Spaces with no Analytic Discs

2019 ◽  
pp. 1-18
Author(s):  
Alexander J. Izzo ◽  
Dimitris Papathanasiou
Keyword(s):  
Maximal Ideal ◽  
Uniform Algebra ◽  
Maximal Ideal Space ◽  
Ideal Space ◽  
Regular Space ◽  
Compact Set ◽  
Gleason Part ◽  
Completely Regular ◽  
Analytic Discs ◽  
Compact Subspace

Abstract We strengthen, in various directions, the theorem of Garnett that every $\unicode[STIX]{x1D70E}$ -compact, completely regular space $X$ occurs as a Gleason part for some uniform algebra. In particular, we show that the uniform algebra can always be chosen so that its maximal ideal space contains no analytic discs. We show that when the space $X$ is metrizable, the uniform algebra can be chosen so that its maximal ideal space is metrizable as well. We also show that for every locally compact subspace $X$ of a Euclidean space, there is a compact set $K$ in some $\mathbb{C}^{N}$ so that $\widehat{K}\backslash K$ contains a Gleason part homeomorphic to  $X$ , and $\widehat{K}$ contains no analytic discs.

scholarly journals The asymptotics of the analytic torsion on CR manifolds with S1 action

2019 ◽  
Vol 21 (04) ◽  
pp. 1750094 ◽  
Author(s):  
Chin-Yu Hsiao ◽  
Rung-Tzung Huang
Keyword(s):  
Line Bundle ◽  
Asymptotic Formula ◽  
Analytic Torsion ◽  
Cr Manifold ◽  
Cr Manifolds ◽  
Dimension Formula ◽  
Positive Line Bundle ◽  
Positive Line

Let [Formula: see text] be a compact connected strongly pseudoconvex CR manifold of dimension [Formula: see text], [Formula: see text] with a transversal CR [Formula: see text]-action on [Formula: see text]. We introduce the Fourier components of the Ray–Singer analytic torsion on [Formula: see text] with respect to the [Formula: see text]-action. We establish an asymptotic formula for the Fourier components of the analytic torsion with respect to the [Formula: see text]-action. This generalizes the asymptotic formula of Bismut and Vasserot on the holomorphic Ray–Singer torsion associated with high powers of a positive line bundle to strongly pseudoconvex CR manifolds with a transversal CR [Formula: see text]-action.

scholarly journals The Bochner-flat cone of a CR manifold

2008 ◽  
Vol 144 (3) ◽  
pp. 747-773
Author(s):  
Liana David
Keyword(s):  
Open Subset ◽  
Kähler Manifold ◽  
Parameter Family ◽  
Local Geometry ◽  
Cr Manifold ◽  
Kähler Structure ◽  
Complex Dimension ◽  
Kahler Manifold ◽  
Pseudo Convex

AbstractWe construct a Kähler structure (which we call a generalised Kähler cone) on an open subset of the cone of a strongly pseudo-convex CR manifold endowed with a one-parameter family of compatible Sasaki structures. We determine those generalised Kähler cones which are Bochner-flat and we study their local geometry. We prove that any Bochner-flat Kähler manifold of complex dimension bigger than two is locally isomorphic to a generalised Kähler cone.

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