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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…
Convexity of asymptotic geodesics in Hilbert Geometry
Charalampos Charitos, Ioannis Papadoperakis, Georgios Tsapogas
If is the interior of a convex polygon in and two asymptotic geodesics, we show that the distance function $d\left(f\left(t\right),g\left(t\right)\right)…