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| 研究生： |
王必欣 Wang, Pi-Hsin |
|---|---|
| 論文名稱： |
調和函數與完備流形的結構 Harmonic Functions and the Structure of Complete Manifolds |
| 指導教授： |
林君恆
Lam, Kwan-Hang |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系應用數學碩博士班 Department of Mathematics |
| 論文出版年： | 2009 |
| 畢業學年度： | 97 |
| 語文別： | 英文 |
| 論文頁數： | 42 |
| 中文關鍵詞： | 流形末端 |
| 外文關鍵詞： | ends |
| 相關次數： | 點閱：37 下載：1 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
這篇報告的重點是在討論有關完備流形上的調和函數並且應用調和函數空間的維度去估計流形末端(定義3.2)的個數。
This report gives weight to study the harmonic functions on complete manifolds and apply the dimensions of various spaces of harmonic functions to estimate the number of ends (Definition 3.2) of a manifold.
1.Peter Li and Luen-Fai Tam, Symmetric Green's functions on complete manifolds, American Journal of Mathematics 109(1987), 1129-1154.
2.Peter Li and Luen-Fai Tam, Harmonic functions and the structure of complete manifolds, J. Differential Geometry 35(1992), 359-383.
3.Chiung-Jue Sung, Luen-Fai Tam and Jiaping Wang, Spaces of harmonic functions, J. London Math. Soc. (2)61(2000), 789-806.
4.S. Y. Cheng and S. T. Yau, Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math, 28(1975), 333-354.
5.Peter Li and Jiaping Wang, Complete manifolds with positive spestrum, J. Differential Geometry 58(2001), 501-534.
6.S. T. Yau, Harmonic functions on complete Riemannian
manifolds, Proc. JDG Conference (to appear).
7.Peter Li, Curvature and function theory on Riemannian manifolds, International Press(2000),375-432.
8.Peter Li, Harmonic functions and applications to complete manifolds, preprint.
9.Peter Li, Lecture notes on geometric analysis, preprint.
10.Peter Li, Harmonic sections of polynomial growth, Mathematical Research Letters 4(1997),35-44.
2009-07-01公開