31 citations · 43 across the 23 of their papers we have counts for
24 papers · 1 filter
On the Teichm{ü}ller space of acute triangles
Hideki Miyachi, Ken'Ichi Ohshika, Athanase Papadopoulos
We continue the study of the analogue of Thurston's metric on the Teichm{ü}ller space of Euclidean triangle which was started by Saglam and Papadopoulos in [1].By direct calculatio…
Thurston's broken windows only theorem revisited
Ken'ichi Ohshika
The'broken windows only theorem' is the main theorem of the third paper among a series of the paper in which Thurston proved his uniformisation theorem for Haken manifolds. In this…
Thurston's Bounded image theorem
Cyril Lecuire, Ken'ichi Ohshika
Thurston's bounded image theorem is one of the key steps in his proof of the uniformisation theorem for Haken manifolds. Thurston never published its proof, and no proof has been k…
The infinitesimal and global Thurston geometry of Teichm{ü}ller space
Yi Huang, Ken'Ichi Ohshika, Athanase Papadopoulos
We undertake a systematic study of the infinitesimal geometry of the Thurston metric, showing that the topology, convex geometry and metric geometry of the tangent and cotangent sp…
Realisation of bending measured laminations by Kleinian surface groups
Shinpei Baba, Ken'ichi Ohshika
For geometrically finite Kleinian surface groups, Bonahon and Otal proved the existence part, and partly the uniqueness part of the bending lamination conjecture. In this paper, we…
A glimpse into Thurston's work
Ken'Ichi Ohshika, Athanase Papadopoulos
We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the traditi…
Shapes of hyperbolic triangles and once-punctured torus groups
Sang-hyun Kim, Thomas Koberda, Jaejeong Lee +3
Let be a hyperbolic triangle with a fixed area . We prove that for all but countably many , generic choices of have the property that the group generated by the --…
Classification of non-free Kleinian groups generated by two parabolic transformations
Hirotaka Akiyoshi, Ken'ichi Ohshika, John Parker +2
We give a full proof to Agol's announcement on the classification of non-free Kleinian groups generated by two parabolic transformations.
Bijections of geodesic lamination space preserving left Hausdorff convergence
Ken'Ichi Ohshika, Athanase Papadopoulos
We introduce an asymmetric distance function, which we call the `left Hausdorff distance function', on the space of geodesic laminations on a closed hyperbolic surface of genus at…
Homeomorphisms and intersection number
Ken'Ichi Ohshika, Athanase Papadopoulos
We prove two rigidity results for automorphism groups of the spaces ML(S) of measured laminations on a closed hyperbolic surface S and PML(S) of projective measured laminations on…
Discontinuous motions of limit sets
Mahan Mj, Ken'ichi Ohshika
We characterise completely when limit sets, as parametrised by Cannon-Thurston maps, move discontinuously for a sequence of algebraically convergent quasi-Fuchsian groups.
Measurable Rigidity for Kleinian groups
Woojin Jeon, Ken'ichi Ohshika
Let be two Kleinian groups with homeomorphic quotients and . We assume that is of divergence type, and consider the Patterson-Sullivan mea…
Primitive stable closed hyperbolic 3-manifolds
Inkang Kim, Cyril Lecuire, Ken'ichi Ohshika
We show that closed 3-manifolds with high Heegaard distance and bounded subsurface Heegaard distance are primitive stable when they are regarded as representations from the free gr…
Subgroups of mapping class groups related to Heegaard splittings and bridge decompositions
Ken'ichi Ohshika, Makoto Sakuma
Let be a Heegaard splitting of a closed orientable 3-manifold (or a bridge decomposition of a link exterior). Consider the subgroup of t…
Conical limit sets of hyperbolic subgroups
Woojin Jeon, Ken'ichi Ohshika
Given a hyperbolic subgroup of a hyperbolic group for which a Cannon-Thurston map $\hat i:\partial H \ra \partial G$ exists, we study the limit set of with respec…
A note on the rigidity of unmeasured lamination spaces
Ken'ichi Ohshika
We show that every auto-homeomorphism of the unmeasured lamination space of an orientable surface of finite type is induced by a unique extended mapping class unless the surface is…
Reduced Bers boundaries of Teichmüller spaces
Ken'ichi Ohshika
We consider a quotient space of the Bers boundary of Teichmüller space, which we call the reduced Bers boundary, by collapsing each quasi-conformal deformation space into a point.…
Divergence, exotic convergence and self-bumping in quasi-Fuchsian spaces
Ken'ichi Ohshika
In this paper, we study the topology of the boundaries of quasi-Fuchsian spaces. We first show for a given convergent sequence of quasi-Fuchsian groups, how we can know the end inv…
Primitive stable representations of free Kleinian groups
W. Jeon, I. Kim, K. Ohshika with C. Lecuire
In this paper, we give a complete criterion for a discrete faithful representation $ρ:F_n \ra \pslc$ to be primitive stable. This will answer Minsky's conjectures about geometric c…
Geometry and topology of geometric limits I
Ken'ichi Ohshika, Teruhiko Soma
In this paper, we classify completely hyperbolic 3-manifolds corresponding to geometric limits of Kleinian surface groups isomorphic to for a finite-type hyperbolic surfac…
Constructing geometrically infinite groups on boundaries of deformation spaces
Ken'ichi Ohshika
Consider a geometrically finite Kleinian group without parabolic or elliptic elements, with its Kleinian manifold $M=(\H^3\cup Ω_G)/G$. Suppose that for each boundary component…
Convergence of freely decomposable Kleinian groups
Inkang Kim, Cyril Lecuire, Ken'ichi Ohshika
We consider a compact orientable hyperbolic 3-manifold with a compressible boundary. Suppose that we are given a sequence of geometrically finite hyperbolic metrics whose conformal…
Realising end invariants by limits of minimally parabolic, geometrically finite groups
Ken'ichi Ohshika
We shall show that for a given homeomorphism type and a set of end invariants (including the parabolic locus) with necessary topological conditions which a topologically tame Klein…
Divergent sequences of Kleinian groups
Ken'ichi Ohshika
One of the basic problems in studying topological structures of deformation spaces for Kleinian groups is to find a criterion to distinguish convergent sequences from divergent seq…