We apply a spherical CR Dehn surgery theorem in order to obtain infinitely many Dehn surgeries of the Whitehead link complement that carry spherical CR structures. We consider as starting point the spherical CR uniformization of the Whitehead link complement constructed by Parker and Will, using a Ford domain in the co…
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10 results for “CR-uniformization”
3-manifolds are CR uniformized on spheres, proving a conjecture.
problem Uniformizing 3-manifolds with cusps using CR methods.
method Spherical CR uniformization of complex hyperbolic triangle groups.
result Magic 3-manifolds and other cusped 3-manifolds are CR uniformizable.
We describe a simple fundamental domain for the holonomy group of the boundary unipotent spherical CR uniformization of the figure eight knot complement, and deduce that small deformations of that holonomy group (such that the boundary holonomy remains parabolic) also give a uniformization of the figure eight knot comp…
We explore the limit set of a particular spherical CR uniformization of a cusped hyperbolic manifold. We prove that the limit set is the closure of a countable union of -circles, is connected, and contains a Hopf link with three components; we also show that the fundamental group of its complement in …
We consider the discrete representations of 3-manifold groups into that appear in the Falbel-Koseleff-Rouillier census, such that the peripheral subgroups have cyclic unipotent holonomy. We show that two of these representations have conjugate images, even though they represent different 3-manifold groups. Th…
Slim curves on 3-sphere help spherical CR uniformizations.
problem Understanding curves on 3-sphere for CR uniformizations.
method Defining slimness, analyzing foliations, and applying to quasi-Fuchsian groups.
result Slim curves lead to spherical CR uniformizations of certain 3-manifolds.
Complex hyperbolic triangle groups yield specific 3-manifolds at infinity.
problem Characterizing manifolds at infinity of complex hyperbolic orbifolds.
method Spherical CR uniformization and Dehn surgery.
result Specific 3-manifolds at infinity of complex hyperbolic triangle groups are identified.
Study reveals hidden accidental parabolics in complex hyperbolic geometry.
problem Understanding hidden parabolics in complex hyperbolic geometry.
method New technique to show ideal boundary of Ford domain is an infinite-genus handlebody.
result 3-manifold at infinity of is the complement of chain link .
Researchers found a new hyperbolic 3-orbifold using a Menger curve.
problem Constructing a new hyperbolic 3-orbifold with specific properties.
method Discovered a discrete, convex cocompact and faithful representation of a hyperbolic group into PU(2,1).
result The 3-orbifold at infinity of the representation is a closed hyperbolic 3-orbifold.
In this note, we mainly focus on the existence of pseudo-Einstein contact forms, an upper bound eigenvalue estimate for the CR Paneitz operator and its applications to the uniformization theorem for Sasakian space form in an embeddable closed strictly pseudoconvex CR 3-manifold. Firstly, the existence of pseudo-Einstei…