Research on Martin and Kuranochi boundaries of covering surfaces

覆盖面Martin和Kuranochi边界研究

• 批准号: 10640192
• 负责人: MASAOKA Hiroaki
• 金额: $ 1.73万
• 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: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640192/
• 关键词: Martin boundary; harmonic function; unlimited covering surface; minimal fine topology; conformal imbedding; nonlinar partial equation of hyperbolic type; parabolic equation; mean value property; 有界調和関数; 縮約極値的長さ; 1階非線型双曲型方程式; 波動方程式; α階放物型方程式

(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.

(1)他给了一个平均值性质的多温度。1。马丁边界和调和函数。正冈共同获得与Segawa以下结果。(1)他们给出了在一个单片的无限Riemann曲面上的正调和函数空间与其基曲面相同的充要条件，并对有界调和函数空间也给出了同样的充要条件. (2)确定了以穿孔黎曼球面为基曲面的Heins覆盖曲面的Martin边界。(3)对于开的黎曼曲面R、R的单片无限覆盖曲面R的极小边界点P，利用极小精细拓扑给出了P上R的极小边界点的个数的一个刻画.共形嵌入。石田获得了以下结果。(1)对于一个平面区域R，他给出了环R共形嵌入的模的范围。(2)通过减少极值长度，他讨论了从连通平面区域到圆盘的共形嵌入.非线性双曲型偏微分方程。Tsuji获得了以下结果。(1)他给出了一个必要和充分条件的可积性二阶非线性方程的双曲型描述表面负高斯曲率。(2)在一定条件下讨论了2×2双曲型一阶非线性偏微分方程组Cauchy问题整体解的存在性.平均值性质与最小值原理。西尾得到了以下结果。(2)他给出了多超温的极小值原理。(3)他给了一个平均值财产的解决方案的波动方程。(4)他给出了α阶抛物方程解的一个均值性质。

项目成果

瀬川重男,正岡弘照: "C＼{0} の有限葉非有界被覆面のMartin境界"数理解析研究所講究録. 1116. 29-37 (1999)

Shigeo Sekawa、Hiroteru Masaoka：“C{0} 的有限叶无界覆盖表面的马丁边界”数学分析研究所 1116. 29-37 (1999)。

M. Nishio, K. Shimomura and N. Suzuki: "A mean value property of poly-temperatures on a strip domain"J. London Math. Soc.. 58. 381-393 (1998)

M. Nishio、K. Shimomura 和 N. Suzuki：“带状域上多温度的均值性质”J。

M. Nishio, K.Shimomura and N. Suzuki: "Note on poly-supertemperatures on a strip domain"Osaka J. Math.. (掲載予定).

M. Nishio、K.Shimomura 和 N. Suzuki：“带状域上的多超温注释”Osaka J. Math..（待出版）。

M. Nishio, T. Sugimoto and N. Suzuki: "Mean value properties for the wave equation"9th Int. Coll. on Differential Equ.(ed. D. Bainov). 289-292 (1999)

M. Nishio、T. Sugimoto 和 N. Suzuki：“波动方程的平均值性质”第 9 期 Int。

M. Nishio and N. Suzuki: "A characterization of strip domains by a mean value property for the parabolic operator of order α"New Zealand Math. J.. (掲載予定).

M. Nishio 和 N. Suzuki：“通过 α 阶抛物线算子的平均值属性来表征带状域”新西兰数学杂志 (New Zealand Math J.)。