Minimal surfaces in germs of hyperbolic 3–manifolds
نویسنده
چکیده
This article introduces a universal moduli space for the set whose archetypal element is a pair that consists of a metric and second fundamental form from a compact, oriented, positive genus minimal surface in some hyperbolic 3–manifold. This moduli space is a smooth, finite dimensional manifold with canonical maps to both the cotangent bundle of the Teichmüller space and the space of SO3(C) representations for the given genus surface. These two maps embed the universal moduli space as a Lagrangian submanifold in the product of the latter two spaces. AMS Classification 53C42, 53A10; 53D30
منابع مشابه
Minimal Surfaces in Geometric 3-manifolds
In these notes, we study the existence and topology of closed minimal surfaces in 3-manifolds with geometric structures. In some cases, it is convenient to consider wider classes of metrics, as similar results hold for such classes. Also we briefly diverge to consider embedded minimal 3-manifolds in 4-manifolds with positive Ricci curvature, extending an argument of Lawson to this case. In the ...
متن کاملProblems around 3–manifolds
This is a personal view of some problems on minimal surfaces, Ricci flow, polyhedral geometric structures, Haken 4–manifolds, contact structures and Heegaard splittings, singular incompressible surfaces after the Hamilton–Perelman revolution. We give sets of problems based on the following themes; Minimal surfaces and hyperbolic geometry of 3–manifolds. In particular, how do minimal surfaces gi...
متن کاملMinimal Surfaces in Finite Volume Hyperbolic 3-manifolds N and in M × S, M a Finite Area Hyperbolic Surface
We consider properly immersed finite topology minimal surfaces Σ in complete finite volume hyperbolic 3-manifolds N , and in M × S, where M is a complete hyperbolic surface of finite area. We prove Σ has finite total curvature equal to 2π times the Euler characteristic χ(Σ) of Σ, and we describe the geometry of the ends of Σ. .
متن کاملThe Cauchy Problem of Lorentzian Minimal Surfaces in Globally Hyperbolic Manifolds
In this note a proof is given for global existence and uniqueness of minimal Lorentzian surface maps from a cylinder into globally hyperbolic Lorentzian manifolds for given initial values up to the first derivatives.
متن کاملGlobal Existence and Uniqueness of Minimal Surfaces in Globally Hyperbolic Manifolds
In this note a proof is given for global existence and uniqueness of minimal surfaces of Lorentzian type from a cylinder into certain Lorentzian manifolds for given initial values up to the first derivatives.
متن کامل