Boundary behavior of analytic functions and harmonic functions

1.Segawa证明了正边界的开Riemann曲面的有限张无限覆盖曲面上的每一个正调和函数都是通过投影映射对基曲面上的正调和函数的拉回当且仅当覆盖曲面的Martin紧化通过投影映射与基曲面的Martin紧化同构。Segawa证明了有界调和函数在Martin边界下的类似结果。Segawa确定了复平面上m-Sheet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&lt；p&lt；d的Royden p-紧化是同胚的当且仅当这两个黎曼流形之间存在几乎等距同胚。2.Nakai和Tada确定了旋转自由密度的最大增长，这是Picard原理的一个例外扰动。Tada和Nakai证明了如果Picard原理对于旋转自由密度P是有效的，那么存在一个本质集P，它在某种意义上是任意小的和稀有的。3.Nakai和Tada证明了Liouville定理在一类适当含有多重调和函数的函数上的推广。4.上田证明了对于一个完整函数族，该族中每个函数的零点都是奇数阶的。上田推广了内万林纳的三函数定理。5.Narita给出了有界域的一个充分条件，使得调和插值序列也是插值序列。Narita给出了有界域无不规则边界点的一个充分条件，使得存在一个调和插值序列，它不是插值型的。Nakai证明了唯一性定理是发生Myrberg现象的充分条件，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.