改良Ahlfors不等式

改良Ahlfors不等式 IMPROVEMENT OF Ahlfors INEQUALITY 孙道椿 1 first-author 武汉大学数学系 武汉大学数学系 本文引进了区域的被割率及曲线的被覆率概念,从而对Ahlfors不等式中的常数h作了明确地估计,即得到p + （F） > p（F 0 ）S-64δ —3 L由这个改良不等式,可以改良一系列定理,可以证明代数体函数存在充满圆序列。 In this paper, we estimate for the constant h in Ahlfors fundamental ine- quality. Theorem; Suppose that F 0 is a domain on the unit sphere V, and that the boundary of F 0 are different q points, where the spherical distance of arbi- trary two points is not smaller thanδ∈（0, 1/2）, then for any connected finite covering surface F, we have p+（F）≥p（F 0 ）S-h（δ）L, where p（F） is the Euler characthristic of F, p+=max（0, p）, S is the mean covering number of F 0 , L is the length of the relative boundary of F and is a constant which depends on d only. For example, we may take h（δ）=64δ -3 被割率 被覆率 相对边界 覆盖曲面 Ahlfors不等式 cut ratio covered ratio relative boundary covering surface Ahlfors inequality O174.51 国家自然科学基金资助项目(41275027;11504121) 1992-03-01 2021-04-01 3