论文标题
关于双曲机中最佳圆与不连续组的问题
On Problem of Best Circle to Discontinuous Groups in Hyperbolic Plane
论文作者
论文摘要
本文的目的是描述Bolyai-Lobachevsky双曲线平面中不连续群的基本域中最大的刻有圆圈。我们给出了一些已知的基本事实，该事实与内调型问题和铭文圆圈的存在概念有关。我们研究了G = [3、3、3、3]的最佳圆，每个阶段的旋转中心4个。使用Lagrange乘数方法，我们将描述最含量最佳的圆的特征。该方法可用于G = [3、3、3，...，3]中的更一般情况，通过越来越多的计算，至少4个旋转中心，每个旋转中心至少4个旋转中心。我们通过更几何定理观察到，分别在当量中心和附加的顶点与琐碎的稳定器相等的角度来实现最大半径。定理3将结束我们的论点，即引理3和4扮演关键角色。
The aim of this paper is to describe the largest inscribed circle into the fundamental domains of a discontinuous group in Bolyai-Lobachevsky hyperbolic plane. We give some known basic facts related to the Poincare-Delone problem and the existence notion of the inscribed circle. We study the best circle of the group G = [3, 3, 3, 3] with 4 rotational centers each of order 3. Using the Lagrange multiplier method, we would describe the characteristic of the best-inscribed circle. The method could be applied for the more general case in G = [3, 3, 3,..., 3] with at least 4 rotational centers each of order 3, by more and more computations. We observed by a more geometric Theorem 2 that the maximum radius is attained by equalizing the angles at equivalent centers and the additional vertices with trivial stabilizers, respectively. Theorem 3 will close our arguments where Lemma 3 and 4 play key roles.
