Equality in Laszlo Fejes Toth's triangle bound for hyperbolic surfaces
arXiv:1206.3020
Abstract
For k>6, we determine the minimal area of a compact hyperbolic surface, and an oriented compact hyperbolic surface that can be tiled by embedded regular triangles of angle 2π/k. Based on this, all the cases of equality in Laszlo Fejes Toth's triangle bound for hyperbolic surfaces are described.