2003 Fiscal Year Final Research Report Summary
Ideal boundary of covering surfaces
| Project/Area Number |
14540192
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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, School of Liberal Arts and Sciences, Professor, 教養部, 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)
JIN Naondo Shiga University, Faculty of Education, Lecturer, 教育学部, 講師 (90206368)
NISHIO Masaharu Osaka City University, Graduate school of Science, Associate professor, 大学院・理学研究科, 助教授 (90228156)
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| Project Period (FY) |
2002 – 2003
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| Keywords | finitely sheeted unlimited covering surface / Martin boundary / Kuramochi boundary / quasiconformal mapping / harmonic dimension / Denjoy domain / nonlinear second order hyperbolic equation / caloric morphism |
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| Research Abstract |
1.(1)For a Riemann surface Rand a finitely sheeted unlimited covering surface W of R, by Martin boundaries (resp. Kuramochi boundaries) of Rand W Masaoka obtained jointly with Segawa and Jin necessary and sufficient conditions for the spaces of bounded harmonic functions (resp. harmonic functions with finite Dirichlet integrals) on Rand W being same, and in case R is the unit disc we obtained more results than that in the general case.
(2)In case p = 2,3, for -sheeted unlimited covering surfaces Rand R of C＼{0} which are quasiconformally equivalent to each other, Masaoka showed jointly with Segawa that the harmonic dimension ( the cardinal number of the minimal Martin boundary) of R is equal to that of R'.
(3)For Heins' covering surfaces R and R' of C＼{0} which are quasiconformally equivalent toeach other, Masaoka showed that the harmonic dimension of R is equal to that of R'
2.For a Denjoy domain Gin C with ρ boundary components (ρ≧3) and a Denjoy subdomain G'of G with ρ boundary components, Ishida showed that, if G' is mapped conformally into G by a mapping f preserving each boundary component, f is the identity mapping.
3.Tsuji studied the Cauchy problem for nonlinear second order hyperbolic equations.
4.Segawa studied the type problem for a infinitely sheeted simply connected unlimited covering surface of C.
5.Nishio obtained some characterizations for Caloric morphism brtween manifolds.
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Research Products
(26 results)
