| dc.contributor.advisor | 陳天進 | zh_TW |
| dc.contributor.advisor | Chen, Tian Jin | en_US |
| dc.contributor.author (Authors) | 林群根 | zh_TW |
| dc.contributor.author (Authors) | Lin, Qun Gen | en_US |
| dc.creator (作者) | 林群根 | zh_TW |
| dc.creator (作者) | Lin, Qun Gen | en_US |
| dc.date (日期) | 1995 | en_US |
| dc.date (日期) | 1994 | en_US |
| dc.date.accessioned | 29-Apr-2016 16:00:15 (UTC+8) | - |
| dc.date.available | 29-Apr-2016 16:00:15 (UTC+8) | - |
| dc.date.issued (上傳時間) | 29-Apr-2016 16:00:15 (UTC+8) | - |
| dc.identifier (Other Identifiers) | B2002003515 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/88458 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學系 | zh_TW |
| dc.description.abstract (摘要) | 本文中我們將證明Kobayashi擬度量在凸域中的三角不等式成立，任一C<sup>n</sup>中不包含複仿射線之凸域皆可解析嵌入n維單位多重圓板，在凸域中的Carathéodory距離函數產生原來的拓樸以及在凸域中的hyperbolicity和measure hyperbolicity是等價的概念，進而推論到任一體積有限的凸域必須是hyperbolic，因此，當然是measure hyperbolic。 | zh_TW |
| dc.description.abstract (摘要) | In this thesis , we prove that the triangle inequality of the Kobayashi pseudometric holds in any convex domain. Also , for a convex domain Q containing no complex affine line , we prove that Ω is biholomorphic to a subdomain of the unit polydisc D<sup>n</sup> and the topology induced by the Carathéodory distance function coincides with the Euclidean topology of Ω. Finally , we prove that hyperbolicity and measure hyperbolicity in a convex domain are equivalent. Moreover, any convex domain with finite Euclidean volume must be hyperbolic, therefore , it is measure hyperbolic. | en_US |
| dc.description.abstract (摘要) | 摘要 Abstract Content §0 Introduction-----1 §1 The Poincáre-Bergman Metric in the Unit Disc-----3 §2 The Kobayashi Pseudodistance and Pseudometric-----6 §3 The Carathéodory Pseudodistance and Pseudometric-----11 §4 An Imbedding of Convex Domain into Unit Polydisc-----14 §5 The Topology Induced by the Carathéodory Distance Function-----20 §6 Measure Hyperbolicity and Convexity-----23 | - |
| dc.description.tableofcontents | 摘要 Abstract Content §0 Introduction-----1 §1 The Poincáre-Bergman Metric in the Unit Disc-----3 §2 The Kobayashi Pseudodistance and Pseudometric-----6 §3 The Carathéodory Pseudodistance and Pseudometric-----11 §4 An Imbedding of Convex Domain into Unit Polydisc-----14 §5 The Topology Induced by the Carathéodory Distance Function-----20 §6 Measure Hyperbolicity and Convexity-----23 | zh_TW |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#B2002003515 | en_US |
| dc.title (題名) | 在複n維歐氏空間中有關凸域之不變度量與測度 | zh_TW |
| dc.title (題名) | Invariant metrics and measures on convex domains in C<sup>n</sup> | en_US |
| dc.type (資料類型) | thesis | en_US |
