1999 Fiscal Year Final Research Report Summary
Research on Martin and Kuranochi boundaries of covering surfaces
| Project/Area Number |
10640192
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto Sangyo University |
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Principal Investigator |
MASAOKA Hiroaki Kyoto Sangyo University, Faculty of Science, Professor, 理学部, 教授 (30219315)
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| Co-Investigator(Kenkyū-buntansha) |
SEGAWA 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, 理学部, 助教授 (90228156)
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| Project Period (FY) |
1998 – 1999
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| Keywords | Martin boundary / harmonic function / unlimited covering surface / minimal fine topology / conformal imbedding / nonlinar partial equation of hyperbolic type / parabolic equation / mean value property |
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| Research Abstract |
(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.
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