5 papers
Geometries on Polygons in the unit disc
Charalampos Charitos, Ioannis Papadoperakis, Georgios Tsapogas
For a family of properly embedded curves in the 2-dimensional disk satisfying certain uniqueness properties, we consider convex polygons $P\subset \m…
A specific model of Hilbert geometry on the unit disc
Charalampos Charitos, Ioannis Papadoperakis, Georgios Tsapogas
A new metric on the open 2-dimensional unit disk is defined making it a geodesically complete metric space whose geodesic lines are precisely the Euclidean straight lines. Moreover…
On surfaces with conical singularities of arbitrary angle
Charalampos Charitos, Ioannis Papadoperakis, Georgios Tsapogas
The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the set of closed geodesic…
Generalized Teichmüller space of non-compact 3-manifolds and Mostow rigidity
Charalampos Charitos, Ioannis Papadoperakis
Consider a 3dimensional manifold obtained by gluing a finite number of ideal hyperbolic tetrahedra via isometries along their faces. By varying the isometry type of each tet…
On the Mapping class group of a genus 2 handlebody
Charalampos Charitos, Ioannis Papadoperakis, Georgios Tsapogas
A complex of incompressible surfaces in a handlebody is constructed so that it contains, as a subcomplex, the complex of curves of the boundary of the handlebody. For genus 2 handl…