3 papers
math.MG2020
Ideal Triangulation and Disk Unfolding of a Singular Flat Surface
İsmail Sağlam
An ideal triangulation of a singular flat surface is a geodesic triangulation such that its vertex set is equal to the set of singular points of the surface. Using the fact that ea…
math.MG2020
Classification of punctures on complete flat surfaces
İsmail Sağlam
We investigate the behavior of a complete flat metric on a surface near a puncture. We call a puncture on a flat surface regular if it has a neighborhood which is isometric to that…
math.MG2019
Straightening Billiard Trajectories in Flat Disks and Katok-Zemlyakov Construction
İsmail Sağlam
We provide a method to straighten each billiard trajectory in a flat disk. As an application, we show that for each point on the disk and for almost all directions, the closure of…