2 3 M ay 2 00 5 Immersions of Pants into a Fixed Hyperbolic Surface
نویسنده
چکیده
Exploiting a relationship between closed geodesics on a generic closed hyperbolic surface S and a certain unipotent flow on the product space T 1 (S) × T 1 (S), we obtain a local asymptotic equidistribution result for long closed geodesics on S. Applications include asymptotic estimates for the number of pants immersions into S satisfying various geometric constraints. Also we show that two closed geodesics γ 1 , γ 2 of length close to L chosen uniformly at random have a high probability of partially bounding an immersed 4-holed sphere whose other boundary components also have length close to L.
منابع مشابه
A ug 2 00 5 Immersions of Pants into a Fixed Hyperbolic Surface
Exploiting a relationship between closed geodesics on a generic closed hyperbolic surface S and a certain unipotent flow on the product space T 1 (S) × T 1 (S), we obtain a local asymptotic equidistribution result for long closed geodesics on S. Applications include asymptotic estimates for the number of pants immersions into S satisfying various geometric constraints. Also we show that two clo...
متن کاملM ar 2 00 3 Immersions of Arbitrary Constant Mean Curvature in Hyperbolic Space H 3 ( − 1 )
Our work studies immersions of arbitrary constant mean curvature in H3(−1), as integrable surfaces (i.e., associate families of surfaces). We first present new results related to isometric deformations within this category of surfaces. Next, we give a Weierstrass type representation formula for these immersions. Ultimately, we discuss correspondences between such immersions in Euclidean 3-space...
متن کاملm at h . G T ] 2 3 M ay 2 00 8 SINGULAR SURFACES , MOD 2 HOMOLOGY , AND HYPERBOLIC VOLUME , II
If g is an integer ≥ 2, and M is a closed simple 3-manifold such that π1(M) has a subgroup isomorphic to a genus-g surface group and dimZ2 H1(M ;Z2) ≥ max(3g−1, 6), we show that M contains a closed, incompressible surface of genus at most g. As an application we show that if M is a closed orientable hyperbolic 3-manifold such that VolM ≤ 3.08, then dimZ2 H1(M ;Z2) ≤ 5.
متن کامل2 4 M ay 2 00 5 Cohomogeneity one actions on noncompact symmetric spaces of rank one
We classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the complex hyperbolic spaces CH, n ≥ 3. For the quaternionic hyperbolic spaces HH, n ≥ 3, we reduce the classification problem to a problem in quaternionic linear algebra and obtain partial results. For real hyperbolic spaces, this classificatio...
متن کاملar X iv : m at h / 05 05 24 4 v 1 [ m at h . G T ] 1 2 M ay 2 00 5 WORD HYPERBOLIC EXTENSIONS OF SURFACE GROUPS
Let S be a closed surface of genus g ≥ 2. A finitely generated group Γ S is an extension of the fundamental group π 1 (S) of S if π 1 (S) is a normal subgroup of Γ S. We show that the group Γ S is hyperbolic if and only if the orbit map for the action of the quotient group Γ = Γ S /π 1 (S) on the complex of curves is a quasi-isometric embedding.
متن کامل