Research on Martin and Kuranochi boundaries of covering surfaces

（1）他为多元理论提供了一个平均值属性。1.马丁边界和和谐函数。Masaoka与Segawa共同获得了以下结果。（1）他们给了一个有限的、无限的Riemann表面空间的位置谐波函数的必要和充分的条件，以及它的基础表面是相同的，并且是因为边界谐波函数空间的位置。（2）确定了海因斯'覆盖表面的马丁边界，即其基础表面，即穿孔的里曼球体。（3）对于一个开放的Riemann表面R，一个有限的、无限制的覆盖表面R-D4的R和一个最小边界点p的R，由最小精细拓扑构成，他们赋予了R-D4的数量的最小边界点的字符化。Conformally Inbeddings。Ishida获得了以下结果。（1）对于一个平面区域R，他给了模块的范围，其中R是嵌入式的。（2）通过减小极限长度他从有限连接的平面区域进入磁盘的共正规嵌入。hyperbolic type的非线性部分差异等价物。Tsuji获得了以下结果。（1）他给出了一个必要的和适当的条件，用于二阶非线性方程的超自然类型的描述表面的非线性方程的集成。（2） He discussed the existence of global solutions to the Cauchy problem for 2×2 hyperbolic systems of first order nonlinear partial differential equations with some conditions. 4。平均价值属性和最低原则。Nishio获得了以下结果。（2）他给了多重超温度的最低原则。（3）他给了波浪方程解决方案的一个平均值属性。（4）他给了一个平均值属性来解决Parabolic equation的问题。

(1) He gave a mean value property for poly-temerature.1.Martin boundary and harmonic functions.Masaoka obtained jointly with Segawa the following results.(1) They gave a necessary and sufficient condition for the spaces of positive harmonic functions on a finitely sheeted unlimited Riemann surface and its base surface being same, and did that for the spaces of bounded harmonic functions.(2) The determined the Martin boundaries of Heins' covering surfaces with the punctured Riemann sphere as its base surfaces.(3) For an open Riemann surface R, a finitely sheeted unlimited covering surface RィイD4-ィエD4 of R and a minimal boundary point p of R, by minimal fine topology, they gave a characterization of the number of minimal bounday points of RィイD4-ィエD4 over p.2. Conformally imbeddings. Ishida obtained the following results.(1) For a plane region R, he gave the range of modules for annuli which R is imbedded conformally into.(2) By reduced extremal length he discussed conformal imbeddings from finitely connected plane regions into disks.3. Nonlinear partial differential equations of hyperbolic type. Tsuji obtained the following results.(1) He gave a necessary and sufficient condition for integrability of second order nonlinear equations of hyperbolic type which describe surfaces with negative Gaussian curvature.(2) He discussed the existence of global solutions to the Cauchy problem for 2×2 hyperbolic systems of first order nonlinear partial differential equations with some conditions.4. Mean value property and minimum principle. Nishio obtained the following results.(2) He gave a minimum principle for poly-supertemeratures.(3) He gave a mean value property for solutions of the wave equation.(4) He gave a mean value property for solution of parabolic equation of order α.