CONFORMAL INVARIANTS AND FUNCTION-THEORETIC NULL-SETS
CONFORMAL INVARIANTS AND FUNCTION-THEORETIC NULL-SETS
复制标题
DOI：
10.1007/bf02392634
复制
发表时间：
1950-01-01
期刊：
影响因子：
3.7
通讯作者：
BEURLING, A
中科院分区：
文献类型：
--
作者：
AHLFORS, L;BEURLING, A
最有用的共形不变量是通过求解共形不变极值问题得到的。它们之所以有用，是因为它们必须自动满足多数原则。这类问题的种类繁多，如果我们力求完整，本文的篇幅将达到令人生畏的地步。因此，我们将把自己限制在几个特别简单的不变量上，并相当详细地研究它们的性质和相互关系，每一类不变量都与一个零集范畴相联系，正是由于这个事实，零集自然地进入了函数论的考虑。空集是某个共形不变量退化的区域的补集。不变量之间的不等式导致相应的空集类之间的包含关系。
The most useful conformal invariants are obtained by solving conformMly invariant extremal problems. Their usefulness derives from the fact that they must automatically satisfy a principle of majorization. There is a rich variety of such problems, and if we would aim at completeness this paper would assume forbidding proportions. We shall therefore limit ourselves to a few particularly simple invariants and study their properties and interrelations in considerable detail.Each class of invariants is connected with a category of null-sets, which by this very fact enter naturally in function-theoretic considerations. A null-set is the complement of a region for which a certain conformal invariant degenerates. Inequalities between invariants lead to inclusion relations between the corresponding classes of null-sets.