Research on ideal boundaries of open Riemann surfaces

开黎曼曲面理想边界的研究

基本信息

批准号：
12640192
负责人：
TADA Toshimasa
金额：
$ 1.15万
依托单位：
Daido Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

项目摘要

Martin ideal boundaries. Tada and Nakai showed that the magnitude of an essential set of a density can be prescribed in advance to a certain extent if the Picard principle is valid for the density. Imai proved that the Picard dimension of a signed measure of quasi Kato class is positive if and only if a quadratic form induced by a Schrodinger operator with the measure of its potential is positive definite. Royden ideal boundaries. Nakai and Tada proved the existence of two Riemannian manifolds or even two Euclidean domains such that these two domains are homeomorphic, their two Royden algebras are ring isomorphic, their two Royden compactifications are homeomorphic, and yet they are not almost quasiconformally equivalent. Boundary behabior of harmonic functions. Segawa constructed a covering surface D and a projection (ψ of the unit disk D satisfying HB(D)oψ= HB(D) and HP(D)oψ≠HP(D). Segawa completely determined the topological structure of the Martin boundaries of 3-sheeted covering surfaces of Heins type including minimal boundaries. Nakai constructed an infinitely sheeted covering surface of the complex plane which is a Heins surface such that the harmonic dimension of it is the cardinal number of the continuum. Value distribution theory of meromorphic functions. Ueda solved the Problem 2.27 in Hayman's book in a special case. Ueda proved an improvement of Gundersen's 2-2 theorem by Muess. Point separation by bounded analytic functions and theory of function algebra. Narita gave a sufficient condition for existence of harmonic interpolating but not interpolating sequence in a plane region. Narita considered a sequence in a plane region such that the infimum of the diameter of the complement of the region is positive and divided the sequence into two sequences. He showed that the sequence is an interpolating sequence if the closure of two divided sequences are disjoint in the maximal ideal space.

马丁理想边界。 Tada和Nakai表明，如果PICARD原理对密度有效，则可以在一定程度上提前规定一组密度的大小。 IMAI证明，当且仅当Schrodinger操作员诱导的具有其电势测量的二次形式的二次形式时，且仅当其电势的测量值的PICARD尺寸是正定义的。罗伊登理想边界。 Nakai和Tada证明了存在两个Riemannian歧管，甚至存在两个欧几里得领域，因此这两个领域是同构的，他们的两个Royden代数是环形同构的，它们的两个Royden紧凑型是同音的，但它们几乎不是quasicicicconic的等值。谐波函数的边界。 Segawa构建了一个覆盖面D和一个投影（单位盘的ψ满足Hb（D）Oψ= Hb（d）和HP（D）Oψ≠HP（D）。Segawa完全确定了Martin offlane suplane sanffert of Surplate sanffert of Mirimalalies of neftible nifinity nifinifine n Infinine of Infinine a的拓扑结构。表面是连续的谐波数量，在特殊情况下，ueda函数的价值分布理论在Hayman的书中解决了。在平面区域中插值序列。他表明，如果两个分隔序列的闭合在最大理想空间中是不相交的，则该序列是插值序列。