ON THE AREAS OF THE MINIMAL TRIANGLES IN VEECH SURFACES  

作　　者：Yumin ZHONG 钟裕民(School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China)

机构地区：[1]School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China

出　　处：《Acta Mathematica Scientia》2020年第2期503-514,共12页数学物理学报（B辑英文版）

基　　金：Supported by National Natural Science Foundation of China(11701039);Youth and Research and Innovation Program of BUPT(2017RC18)。

摘　　要：Smillie and Weiss proved that the set of the areas of the minimal triangles of Veech surfaces with area 1 can be arranged as a strictly decreasing sequence{an}.And each an in the sequence corresponds to finitely many affine equivalent classes of Veech surfaces with area 1.In this article,we give an algorithm for calculating the area of the minimal triangles in a Veech surface and prove that the first element of{an}which corresponds to non arithmetic Veech surfaces is(5-√5)/20,which is uniquely realized by the area of the minimal triangles of the normalized golden L-shaped translation surface up to affine equivalence.

关 键 词：Veech surfaces minimal triangles non arithmetic 

分 类 号：O186.12[理学—数学]