scholarly journals CR embeddability of quotients of the Rossi sphere via spectral theory

2022 ◽  
Author(s):  
Henry Bosch ◽  
Tyler Gonzales ◽  
Kamryn Spinelli ◽  
Gabe Udell ◽  
Yunus E. Zeytuncu
Keyword(s):  
Asymptotic Distribution ◽  
Spectral Theory ◽  
Unit Sphere ◽  
Point Spectrum ◽  
Cr Manifold ◽  
Cr Manifolds ◽  
Cr Structure ◽  
Finite Subgroups

We look at the action of finite subgroups of SU(2) on [Formula: see text], viewed as a CR manifold, both with the standard CR structure as the unit sphere in [Formula: see text] and with a perturbed CR structure known as the Rossi sphere. We show that quotient manifolds from these actions are indeed CR manifolds, and relate the order of the subgroup of SU(2) to the asymptotic distribution of the Kohn Laplacian’s eigenvalues on the quotient. We show that the order of the subgroup determines whether the quotient of the Rossi sphere by the action of that subgroup is CR embeddable. Finally, in the unperturbed case, we prove that we can determine the size of the subgroup by using the point spectrum.

Existence Results for the Prescribed Webster Scalar Curvature on Higher Dimensional CR Manifolds

2013 ◽  
Vol 13 (3) ◽  
Author(s):  
Ridha Yacoub
Keyword(s):  
Scalar Curvature ◽  
Unit Sphere ◽  
Existence Results ◽  
Cr Manifold ◽  
Cr Manifolds ◽  
Higher Dimensional ◽  
Webster Scalar Curvature

AbstractThis paper is about prescribing the Webster scalar curvature on a compact CR manifold of dimension 2n+1 ≥ 5, which is locally CR equivalent to the standard CR unit sphere S

STATIONARY DISCS AND GEOMETRY OF CR MANIFOLDS OF CODIMENSION TWO

2001 ◽  
Vol 12 (08) ◽  
pp. 877-890 ◽  
Author(s):  
A. SUKHOV ◽  
A. TUMANOV
Keyword(s):  
Contact Structure ◽  
Cr Manifolds ◽  
Codimension Two ◽  
Strictly Convex ◽  
Cr Structure ◽  
Conormal Bundle ◽  
Convex Hypersurfaces

We give a construction of stationary discs and the indicatrix for manifolds of higher codimension which is a partial analog of L. Lempert's theory of stationary discs for strictly convex hypersurfaces. This leads to new invariants of the CR structure in higher codimension linked with the contact structure of the conormal bundle.

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.

CR Mappings of Circular CR Manifolds

1995 ◽  
Vol 38 (4) ◽  
pp. 396-407
Author(s):  
André Boivin ◽  
Roman Dwilewicz
Keyword(s):  
Finite Number ◽  
Type Equation ◽  
Vector Spaces ◽  
Cr Manifold ◽  
Complex Vector ◽  
Cr Manifolds ◽  
Cr Mappings

AbstractLet M be a circular CR manifold and let N be a rigid CR manifold in some complex vector spaces. The problem of the existence of local CR mappings from M into N is considered. Conditions are given which ensure that the space of such CR mappings depends on a finite number of parameters. The idea of the proof of the main result relies on a Bishop type equation for CR mappings. Roughly speaking, we look for CR mappings from M into N in the form F = (ƒ,g), we assume that g is given, then we find ƒ in terms of g and some parameters, and finally we look for conditions on g. It works independently of assumptions on the Levi forms of M and N, and there is also some freedom on the codimension of the manifolds.

On inverse spectral theory for singularly perturbed operators: point spectrum

2005 ◽  
Vol 21 (6) ◽  
pp. 1871-1878 ◽  
Author(s):  
S Albeverio ◽  
A Konstantinov ◽  
V Koshmanenko
Keyword(s):  
Spectral Theory ◽  
Point Spectrum ◽  
Singularly Perturbed ◽  
Inverse Spectral Theory ◽  
Inverse Spectral

Spectral Theory for the Neumann Laplacian on Planar Domains With Horn-Like Ends

1997 ◽  
Vol 49 (2) ◽  
pp. 232-262 ◽  
Author(s):  
Julian Edward
Keyword(s):  
Large Class ◽  
Continuous Spectrum ◽  
Spectral Theory ◽  
Point Spectrum ◽  
Pure Point ◽  
Pure Point Spectrum ◽  
Singular Continuous Spectrum ◽  
Finite Multiplicity ◽  
Planar Domains ◽  
Neumann Laplacian

AbstractThe spectral theory for the Neumann Laplacian on planar domains with symmetric, horn-like ends is studied. For a large class of such domains, it is proven that the Neumann Laplacian has no singular continuous spectrum, and that the pure point spectrum consists of eigenvalues of finite multiplicity which can accumulate only at 0 or ∞. The proof uses Mourre theory.

scholarly journals AN OBATA-TYPE THEOREM ON A THREE-DIMENSIONAL CR MANIFOLD

2013 ◽  
Vol 56 (2) ◽  
pp. 283-294 ◽  
Author(s):  
S. IVANOV ◽  
D. VASSILEV
Keyword(s):  
Unit Sphere ◽  
Type Theorem ◽  
Three Dimensional ◽  
First Eigenvalue ◽  
Dimensional Manifold ◽  
Type Condition ◽  
Cr Manifold ◽  
The First Eigenvalue ◽  
Paneitz Operator ◽  
Dimensional Unit

AbstractWe prove the CR version of the Obata's result for the first eigenvalue of the sub-Laplacian in the setting of a compact strictly pseudoconvex pseudohermitian three-dimensional manifold with non-negative CR-Paneitz operator which satisfies a Lichnerowicz-type condition. We show that if the first positive eigenvalue of the sub-Laplacian takes the smallest possible value, then, up to a homothety of the pseudohermitian structure, the manifold is the standard Sasakian three-dimensional unit sphere.

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