Boundary behavior of analytic functions and harmonic functions

1. Segawa证明了正边界的开放Riemann曲面的有限层无限覆盖面上的每一个正调和函数都是基面上的正调和函数通过投影映射的回调当且仅当覆盖面的马丁紧化通过投影映射与基面的马丁紧化同构。Segawa在Martin边界下证明了有界调和函数的类似结果。Segawa确定了复平面的m片循环无限覆盖曲面的Martin边界。Nakai证明了两个d维黎曼流形（d【大于或等于】2）的1<p<d的Royden p紧化当且仅当这些黎曼流形之间存在几乎拟等距同胚时是同胚的。2. Nakai和Tada确定了旋转自由密度的最大增长，这是皮卡德原理的一个例外摄动。Tada和Nakai证明了如果Picard原理对旋转自由密度P是有效的，那么存在一个P的本质集合，它在某种意义上是任意小且稀有的。3. Nakai和Tada证明了一类适当包含多谐函数的函数的Liouville定理的推广。4. Ueda证明了对于整个函数族，族中每个函数的零点都是奇阶的。上田推广了Nevanlinna的三函数定理。5. 成田给出了有界域的充分条件，使调和插值序列也是插值序列。Narita给出了无不规则边界点的有界域存在调和插值序列的充分条件。Nakai证明唯一性定理是米尔伯格现象发生的充分条件，但不是必要条件。

1. Segawa showed that every positive harmonic function on a finitely sheeted unlimited covering surface of an open Riemann surface of positive boundary is a pullback of a positive harmonic function on the base surface by the projection map if and only if the Martin compactification of the covering surface is isomorphic to that of the base surface via the projection map. Segawa proved an analogous result of the above for bounded harmonic functions in terms of Martin boundary. Segawa determined the Martin boundaries of m-sheeted cyclic unlimited covering surfaces of the complex plane. Nakai showed that Royden p-compactifications for 1<p<d of two d-dimensional Riemannian manifolds (d【greater than or equal】2) are homeomorphic if and only if there exists a almost quasiisometric homeomorphism between these Riemannian manifolds. 2. Nakai and Tada determined the maximal growth of a rotation free density which is an exceptional perturbation for Picard principle. Tada and Nakai showed that if the Picard principle is valid for a rotation free density P, then there exists an essential set of P which is arbitrarily small and rare in a sense. 3. Nakai and Tada proved an extension of the Liouville theorem for a class of functions which properly contains polyharmonic functions. 4. Ueda showed that for a family of entire functions, the zeros of each function in the family are of odd order. Ueda generalized Nevanlinna's three-function theorem. 5. Narita gave a sufficient condition for bounded domains in order that a harmonic interpolating sequence is also an interpolating sequence. Narita gave a sufficient condition for bounded domains without irregular boundary points in order that there exists a harmonic interpolating sequence which is not interpolating. Nakai showed that the uniqueness theorem is sufficient but not necessary for the occurrence of the Myrberg phenomenon.