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

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.

scholarly journals On far-outlying constant mean curvature spheres in asymptotically flat Riemannian 3-manifolds

2020 ◽  
Vol 2020 (767) ◽  
pp. 161-191
Author(s):  
Otis Chodosh ◽  
Michael Eichmair
Keyword(s):  
Scalar Curvature ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Existence Results ◽  
Asymptotically Flat ◽  
Weingarten Surfaces ◽  
Differential Geom

AbstractWe extend the Lyapunov–Schmidt analysis of outlying stable constant mean curvature spheres in the work of S. Brendle and the second-named author [S. Brendle and M. Eichmair, Isoperimetric and Weingarten surfaces in the Schwarzschild manifold, J. Differential Geom. 94 2013, 3, 387–407] to the “far-off-center” regime and to include general Schwarzschild asymptotics. We obtain sharp existence and non-existence results for large stable constant mean curvature spheres that depend delicately on the behavior of scalar curvature at infinity.

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