Research on Martin and Kuramochi boundaries of covering surfaces

覆盖表面的Martin和Kuramochi边界研究

基本信息

批准号：
12640193
负责人：
MASAOKA Hiroaki
金额：
$ 1.66万
依托单位：
Kyoto Sangyou University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

项目摘要

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.

1。（1）对于Riemann表面R和R和W的Martin界限，Masaoka与Segawa共同获得了R和W的Martin Borgaries r and Masaoka的最终无限的覆盖表面W，这是R and W上有限的谐波功能的必要和足够条件。最小的优质拓扑，Masaoka与Segawa共同获得了w t的最小库拉莫基边界点的特征。 p。（4）对于Riemann表面R和R和W的Kuramochi边界，Masaoka获得了R和W的最终无限的覆盖面W，为R和W上有限的Dirichlet积分的谐波函数空间获得了必要和足够的条件。 Ishida表明，对于具有n个边界组件（n [大于或相等] 3）和具有n个边界组件的Denjoy子域G'的C型c的Denjoy结构域G，因此G'被MAP F，G / F（g'）映射到G中。3。 tsuji研究了非线性双曲线方程的库奇问题。4。 Segawa研究了无限板的类型问题，简单地连接了Riemann Sphere的无限覆盖面5。（1）Nishio给出了α的抛物线方程溶液的平均价值特性。（2）Nishio表明，在适当的条件下，Martin's and Loeb的压缩在Brelot意义上是谐波空间的压缩，它们的和谐边界是一致的。