| Co-Investigator(Kenkyū-buntansha) |
SAGAWA Shigeo Daido Institute of Technology, Faculty of Engineering, Professor, 工学部, 教授 (80105634)
TSUJI Mikio Kyoto Sangyo University, Faculty of Science, Professor, 理学部, 教授 (40065876)
ISHIDA Hisashi Kyoto Sangyo University, Faculty of Science, Professor, 理学部, 教授 (10103714)
NISHIO Masaharu Osaka City University, Faculty of Science, Associate professor, 大学院・理学研究科, 助教授 (90228156)
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| Research Abstract |
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.
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