2023/08/17 by Fu, Kai, Tahar, Guillaume
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2308.08940
We consider a flat metric with conical singularities on the sphere. Assuming no partial sum of angle defects is equal to 2π, we draw on the geometry of immersed disks to obtain an explicit upper bound on the number of saddle connections with at most k self-intersections. We also deduce a bound on their lengths for a surface with a normalized area.