# CR embeddability of quotients of the Rossi sphere via spectral theory

@article{Bosch2022CREO, title={CR embeddability of quotients of the Rossi sphere via spectral theory}, author={Henry Bosch and Tyler Gonzales and Kamryn Spinelli and Gabe Udell and Yunus E. Zeytuncu}, journal={International Journal of Mathematics}, year={2022} }

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…

## References

SHOWING 1-10 OF 34 REFERENCES

Embeddability for three-dimensional CR-manifolds

- Mathematics
- 1990

A question of principal interest in the theory of compact, three-dimensional CR-manifolds is to understand when a given strictly pseudoconvex, CR-structure can be realized by an embedding in C' . We…

On finite subgroups of SU(2), simple Lie algebras, and the McKay correspondence.

- Mathematics, MedicineProceedings of the National Academy of Sciences of the United States of America
- 1984

The problem of how the restriction pi(n)Gamma decomposes into Gamma-irreducibles for any arbitrary n in [unk](+) has an elegant solution in terms of the Coxeter element for the associated Lie algebra.

Spectrum of the Kohn Laplacian on the Rossi sphere

- MathematicsInvolve, a Journal of Mathematics
- 2019

We study the spectrum of the Kohn Laplacian $\square_b^t$ on the Rossi example $(\mathbb{S}^3, \mathcal{L}_t)$. In particular we show that $0$ is in the essential spectrum of $\square_b^t$, which…

Spectra of Kohn Laplacians on spheres

- MathematicsInvolve, a Journal of Mathematics
- 2019

In this note, we study the spectrum of the Kohn Laplacian on the unit spheres in $\mathbb{C}^n$ and revisit Folland's classical eigenvalue computation. We also look at the growth rate of the…

CR Manifolds and the Tangential Cauchy-Riemann Complex

- Mathematics
- 1991

PRELIMINARIES. Differential Forms and Stokes Theorem. Distributions and Curents. Fundamental Solutions for(these symbols are to be used in an equation -----? ? z ---- see note at bottom)and D. Edge…

Introduction to Smooth Manifolds

- Mathematics
- 2002

Preface.- 1 Smooth Manifolds.- 2 Smooth Maps.- 3 Tangent Vectors.- 4 Submersions, Immersions, and Embeddings.- 5 Submanifolds.- 6 Sard's Theorem.- 7 Lie Groups.- 8 Vector Fields.- 9 Integral Curves…

Attaching Analytic Spaces to an Analytic Space Along a Pseudoconcave Boundary

- Mathematics
- 1965

It is sometimes possible to create new mathematics by relaxing by complication the hypotheses of existing theorems so that the proofs still work. That is what has happened in the present case. The…

Hearing the type of a domain in C 2 with the ∂ ¯ -Neumann Laplacian

- Mathematics
- 2008

A smooth bounded pseudoconvex domain in C2 is of finite type if and only if the number of eigenvalues of its a-Neumann Laplacian that are less than or equal to ? has at most polynomial growth as ?…

Hearing pseudoconvexity with the Kohn Laplacian

- Mathematics
- 2004

Abstract.A bounded domain in with connected Lipschitz boundary is pseudoconvex if the bottom of the essential spectrum of the Kohn Laplacian on the space of (0,q)-forms, 1≤q≤n−1, with L2-coefficients…

Partial differential equations in several complex variables

- Mathematics
- 2001

This book is intended as both an introductory text and a reference book for those interested in studying several complex variables in the context of partial differential equations. In the last few…