Research on ideal boundaries of open Riemann surfaces

马丁的理想边界。多田和中井指出，如果皮卡德原理对密度有效，那么密度的本质集的大小可以在一定程度上预先规定。Imai证明了拟Kato类的符号测度的Picard维数是正的当且仅当由Schrodinger算子及其势测度诱导的二次型是正定的.罗伊登理想边界。Nakai和Tada证明了存在两个黎曼流形甚至两个欧几里得域，使得这两个域是同胚的，它们的两个Royden代数是环同构的，它们的两个Royden紧化是同胚的，但它们不是几乎拟共形等价的。调和函数的边界性质。Segawa构造了一个覆盖面D和单位圆盘D的一个投影，满足HB（D）o H = HB（D）和HP（D）o H = HP（D）。Segawa完全确定了Heins型3-sheeted覆盖曲面的Martin边界的拓扑结构，包括极小边界。Nakai构造了复平面的无限片覆盖曲面，该复平面是Heins曲面，使得其调和维度是连续统的基数。亚纯函数的值分布理论。上田在特殊情况下解决了海曼书中的问题2.27。上田证明了Muess的Gundersen 2-2定理的一个改进。有界解析函数的点分离与函数代数理论。Narita给出了平面区域上存在调和插值序列而非插值序列的充分条件。成田认为一个序列在一个平面区域，使该区域的互补的直径的下确界是积极的，并分为两个序列的序列。他表明，该序列是一个插值序列，如果封闭的两个部门的序列是不相交的最大理想空间。

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.