Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQuasi-Fuchsian 3-Manifolds and Metrics on Teichm{u}ller Space
120
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
An almost Fuchsian 3-manifold is a quasi-Fuchsian manifold which contains an incompressible closed minimal surface with principal curvatures in the range of $(-1,1)$. Such a 3-manifold $M$ admits a foliation of parallel surfaces, whose locus in Teichm{u}ller space is represented as a path $gamma$, we show that $gamma$ joins the conformal structures of the two components of the conformal boundary of $M$. Moreover, we obtain an upper bound for the Teichm{u}ller distance between any two points on $gamma$, in particular, the Teichm{u}ller distance between the two components of the conformal boundary of $M$, in terms of the principal curvatures of the minimal surface in $M$. We also establish a new potential for the Weil-Petersson metric on Teichm{u}ller space.
rate research
Read More
In this paper, the Teichm{u}ller spaces of surfaces appear from two points of views: the conformal category and the hyperbolic category. In contrast to the case of surfaces of topologically finite type, the Teichm{u}ller spaces associated to surfaces of topologically infinite type depend on the choice of a base structure. In the setting of surfaces of infinite type, the Teichm{u}ller spaces can be endowed with different distance functions such as the length-spectrum distance, the bi-Lipschitz distance, the Fenchel-Nielsen distance, the Teichm{u}ller distance and there are other distance functions. Unlike the case of surfaces of topologically finite type, these distance functions are not equivalent. We introduce the finitely supported Teichm{u}ller space T f s H 0 associated to a base hyperbolic structure H 0 on a surface $Sigma$, provide its characterization by Fenchel-Nielsen coordinates and study its relation to the other Teichm{u}ller spaces. This paper also involves a study of the Teichm{u}ller space T 0 ls H 0 of asymptotically isometric hyperbolic structures and its Fenchel-Nielsen parameterization. We show that T f s H 0 is dense in T 0 ls H 0 , where both spaces are considered to be subspaces of the length-spectrum Teichm{u}ller space T ls H 0. Another result we present here is that asymptotically length-spectrum bounded Teichm{u}ller space A T ls H 0 is contractible. We also prove that if the base surface admits short curves then the orbit of every finitely supported hyperbolic surface is non-discrete under the action of the finitely supported mapping class group MCG f s $Sigma$ .
We investigate the Teichm{u}ller parameters for a Euclidean multiple BTZ black hole spacetime. To induce a complex structure in the asymptotic boundary of such a spacetime, we consider the limit in which two black holes are at a large distance from each other. In this limit, we can approximately determine the period matrix (i.e., the Teichm{u}ller parameters) for the spacetime boundary by using a pinching parameter. The Teichm{u}ller parameters are essential in describing the partition function for the boundary conformal field theory (CFT). We provide an interpretation of the partition function for the genus two extremal boundary CFT proposed by Gaiotto and Yin that it is relevant to double BTZ black hole spacetime.
In this note, we propose an approach to the study of the analogue for unipotent harmonic bundles of Schmids Nilpotent Orbit Theorem. Using this approach, we construct harmonic metrics on unipotent bundles over quasi-compact Kahler manifolds with carefully controlled asymptotics near the compactifying divisor; such a metric is unique up to some isometry. Such an asymptotic behavior is canonical in some sense.
The paper contains a new proof that a complete, non-compact hyperbolic $3$-manifold $M$ with finite volume contains an immersed, closed, quasi-Fuchsian surface.
We study global aspects of the mean curvature flow of non-separating hypersurfaces $S$ in closed manifolds. For instance, if $S$ has non-vanishing mean curvature, we show its level set flow converges smoothly towards an embedded minimal hypersurface $Gamma$. We prove a similar result for the flow with surgery in dimension 2. As an application we show the existence of monotone incompressible isotopies in manifolds with negative curvature. Combining this result with min-max theory, we show that quasi-Fuchsian and hyperbolic $3$-manifolds fibered over $mathrm{S}^1$ admit smooth entire foliations whose leaves are either minimal or have non-vanishing mean curvature. We also conclude the existence of outermost minimal surfaces for quasi-Fuchsian ends and study their continuity with respect to variations of the quasi-Fuchsian metric.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
