Scalar curvature,mean curvature and harmonic maps to the circle

Annals of Global Analysis and Geometry - We study harmonic maps from a 3-manifold with boundary to $$\mathbb {S}^1$$ and prove a special case of Gromov dihedral rigidity of three-dimensional cubes...     

Divergent sequences of function groups

In this paper we shall prove a divergence theorem for function groups.     

The Goldman and Fock-Goncharov coordinates for convex projective structures on surfaces

Let \({\mathfrak {P}}(S)\) be the space of convex projective structures on a surface S with negative Euler characteristic. Goldman and Bonahon-Dreyer constructed two different sets of global coordinates for \({\mathfrak {P}}(S)\), both associated to a pair of pants decomposition of the surface S. The article explicitly describes the coordinate change between these two parametrizations. Most of the arguments are concentrated in the case where S is a pair of pants, in which case the Bonahon-Dreyer coordinates are actually due to Fock-Goncharov.     

Affine action and Margulis invariant

In this paper, we show that two Zariski dense subgroups consisting of hyperbolic elements in with the same marked Margulis invariant, are conjugate. We also consider in affine deformations an analogue of quasifuchsian deformation of Fuchsian groups.     

Compactification of Strictly Convex Real Projective Structures

In this paper we compactify the space of convex real projective structures, known as Hitchin’s component in a representation variety. We give geometric meanings to the boundary points.Mathematics Subject Classifications (2000). 51M10, 57S25.     

Length spectrum in rank one symmetric space is not arithmetic

In this paper we show that a nonelementary nonparabolic group in a real semisimple Lie group of rank one has the property that the set of translation lengths of hyperbolic elements is not contained in any discrete subgroup of .

     

Marked length rigidity of rank one symmetric spaces and their product

In this paper we show that if two Zariski dense representations, from a group G into Iso(X) where X is rank one symmetric space, have the proportional marked length spectrum, then they are conjugate. As a generalization we show that a Zariski dense representation into the isometry group of the product of rank one symmetric spaces is determined by the marked cross ratio.     

On the Markus conjecture in convex case

Annals of Global Analysis and Geometry - In this paper, we show that any convex affine domain with a nonempty limit set on the boundary under the action of the identity component of the...     

Primitive stable representations of free Kleinian groups

In this paper, we give a complete criterion for a discrete faithful representation ρ: F _n →PSL(2, ?) to be primitive stable. This will answer Minsky’s conjectures about geometric conditions on ?³/ρ(F _n ) regarding the primitive stability of ρ.