Research on Martin and Kuramochi boundaries of covering surfaces

1. (1)对于Riemann曲面R和R的单片无限覆盖曲面W，Masaoka和Segawa利用R和W的Martin边界，得到了R和W上有界调和函数空间相同的一个充分必要条件. (2)Masaoka和Segawa利用极小精细拓扑，对Riemann曲面R、R的单片无限覆盖曲面W和R的极小Kuramochi边界点p，给出了W在p上的极小Kuramochi边界点个数的一个刻划. (3)对于Riemann曲面R，R的无限制覆盖曲面W和R的极小Martin边界点p，Masaoka和Segawa利用极小精细拓扑得到了W在p上的极小Martin边界点个数的一个特征. (4)对于Riemann曲面R和R的无限制覆盖曲面W，Masaoka利用R和W的Kuramochi边界，得到了调和函数空间在R和W上的有限Dirichlet积分相同的充要条件. Ishida证明了，对于C中具有n个边界分支（n ≥ 3）的Denjoy整环G和G中具有n个边界分支的Denjoy子域G'，使得G'通过映射f共形映射到G中，G / f（G '）没有内点. Tsuji研究了非线性双曲型方程的柯西问题. Segawa研究了黎曼球面上无限单连通复盖曲面的型问题. (1)西尾给出了α阶抛物型方程解的一个均值性质。(2)西尾证明，在适当的条件下，Brelot意义下调和空间的Martin紧化和Loeb紧化的调和边界重合.

1. (1) For a Riemann surface R and a finitely sheeted unlimited covering surface W of R, by Martin boundaries of R and W, Masaoka obtained jointly with Segawa a necessary and sufficient condition for the spaces of bounded harmonic functions on R and W being same.(2) For a Riemann surface R, a finitely sheeted unlimited covering surface W of R and a minimal Kuramochi boundary point p of R, by minimal fine topology, Masaoka obtained jointly with Segawa a charcterization of the number of minimal Kuramochi boundary points of W over p.(3) For a Riemann surface R, a finitely sheeted unlimited covering surface W of R and a minimal Martin boundary point p of R, by minimal fine topology, Masaoka obtained jointly with Segawa a characterization of the number of minimal Martin boundary points of W over p.(4) For a Riemann surface R and a finitely sheeted unlimited covering surface W of R, by Kuramochi boundaries of R and W, Masaoka obtained a necessary and sufficient condition for the spaces of harmonic functions with finite Dirichlet integrals on R and W being same.2. Ishida showed that, for a Denjoy domain G in C with n boundary components (n 【greater than or equal】 3) and a Denjoy subdomain G' of G with n boundary components such that G' is mapped conformally into G by a map f, G / f(G') has no interior points.3. Tsuji studied the Cauchy problem for nonlinear hyperbolic equations.4. Segawa studied the type problem for a infinitely sheeted simply connected unlimited covering surface of the Riemann sphere.5. (1) Nishio gave a mean value property for solutions of parabolic equation of order α.(2) Nishio showed that, under an appropriate condition, for the Martin's and Loeb's compactifications of a harmonic space in the sense of Brelot, their harmonic boundaries coincide.