ACTA issues

## Equality in László Fejes Tóth's triangle bound for hyperbolic surfaces

Christophe Bavard, Károly J. Böröczky, Borbála Farkas, István Prok, Lluis Vena

Acta Sci. Math. (Szeged) 77:3-4(2011), 669-679
28/2010

 Abstract. For $k\geq7$, 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 $2\pi /k$. Based on this, all the cases of equality in László Fejes Tóth's triangle bound for hyperbolic surfaces are described. AMS Subject Classification (1991): 51M10, 52C22 Keyword(s): tiling of hyperbolic surfaces Received April 14, 2010, and in revised form January 11, 2011. (Registered under 28/2010.)