Ideal boundary of covering surfaces

覆盖表面的理想边界

• 批准号: 14540192
• 负责人: MASAOKA Hiroaki
• 金额: $ 1.79万
• 依托单位: Kyoto Sangyo University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540192/
• 关键词: finitely sheeted unlimited covering surface; Martin boundary; Kuramochi boundary; quasiconformal mapping; harmonic dimension; Denjoy domain; nonlinear second order hyperbolic equation; caloric morphism; Heins型被覆面; 2階双曲型方程式; ダンジョア領域; 無限葉被覆面; 熱方

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.

1.（1）对于Riemann曲面兰德和R的无限复盖曲面W，分别用Martin边界（Kuramochi边界）的兰德W Masaoka与Segawa和Jin共同获得的有界调和函数空间的充分必要条件（分别为）。在兰德W上的有限Dirichlet积分的调和函数）相同的情况下，得到了比一般情况更多的结果。(2)In在p = 2，3的情形下，对于C {0}的拟共形等价的-片无限覆盖曲面兰德R，Masaoka与Segawa共同证明了R的调和维数（最小Martin边界的基数）等于R '的调和维数.（3）Masaoka证明了C的Heins覆盖曲面R和R'的调和维数与R' 2的调和维数相等。对于C中具有ρ边界分量的Denjoy域G（ρ = 3）和G中具有ρ边界分量的Denjoy子域G '，Ishida证明了，如果G'由一个保各边界分量的映射f保形映射到G中，3.Tsuji研究了二阶非线性双曲型方程的Cauchy问题，4.Segawa研究了C的无限单连通覆盖曲面的型问题，5.Nishio得到了流形之间Caloric态射的一些特征.

项目成果

Hiroaki Masaoka, Naondo Jin: "minimal Kuramochi boundary of finitely sheeted unlimited covering surfaces"RIMS kokyuroku. Vol.1293. 78-83 (2002)

Hiroaki Masaoka、Naondo Jin：“有限片状无限覆盖表面的最小 Kuramochi 边界”RIMS kokyuroku。

Hisashi Ishida, Fumio Maitani: "Conformal imbeddings of Denjoy domains II"Acta Human.Sci.Univ.Sangio Kyotiensis. vol.31. 1-5 (2002)

Hisashi Ishida、Fumio Maitani：“Denjoy 域 II 的保形嵌入”Acta Human.Sci.Univ.Sangio Kyotiensis。

Hiroaki Masaoka, Shigeo Segawa: "Harmonic functions on finitely sheeted unlimited covering"J.Math.Soc.Japan. 55. 323-334 (2003)

Hiroaki Masaoka、Shigeo Sekawa：“有限片无限覆盖上的调和函数”J.Math.Soc.Japan。

Naondo Jin, Hiroaki Masaoka: "Kuramochi boundary and harmonic functions with finite Dirichlet integrals on unlimited covering surfaces"Osaka J.Math.. vol.41. 1-17 (2004)

Naondo Jin、Hiroaki Masaoka：“Kuramochi 边界和调和函数以及无限覆盖表面上的有限 Dirichlet 积分”Osaka J.Math.. vol.41。

N.Jin, H.Masaoka: "Kuramochi boundary and harmonic functions with finite Dirichlet integrals on unlimited covering surfaces"Osaka J.Math.. 141. (2004)

N.Jin，H.Masaoka：“Kuramochi 边界和调和函数，在无限覆盖表面上具有有限 Dirichlet 积分”Osaka J.Math.. 141. (2004)