1 citations · 1 across the 4 of their papers we have counts for
5 papers
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…
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…
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…
Signature Calculation of Area Hermitian Form on Some Spaces of Polygons
İsmail Sağlam
This chapter is motivated by the paper by Thurston on triangulations of the sphere and singular flat metrics on the sphere. Thurston locally parametrized the moduli space of singul…
Flat Surfaces with Finite Holonomy Groups
Ísmail Sağlam
We prove that flow of a generic geodesic on a flat surface with finite holonomy group is ergodic. We use this result to prove that flows of generic billiards on certain flat surfac…