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| 研究生： |
郭仲祐 Guo, Chung-You |
|---|---|
| 論文名稱： |
The Asymptotic Expansion of Green's function on Riemannian Manifolds 格林函數在黎曼流形上的漸近展開 |
| 指導教授： |
張樹城
Chang, Shu-Cheng 宋瓊珠 Sung, Chiung-Jue |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系 Department of Mathematics |
| 論文出版年： | 2009 |
| 畢業學年度： | 97 |
| 語文別： | 英文 |
| 論文頁數： | 24 |
| 中文關鍵詞： | 格林函數 、保角正規坐標 、漸近平滑流形 、保角拉普拉斯算子 、漸近展開 |
| 外文關鍵詞： | Green's function, conformal normal coordinates, aysmptotically flat manifolds, conformal Laplacian, aysmptotic expansion |
| 相關次數： | 點閱：1 下載：0 |
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The main goal in this paper is to report the asymptotic expansion of Green's function of the conformal Laplacian on
a compact Riemannian manifold without boundary. First of all, we introduce the conformal normal coordinates. Second, we discuss the expansion of Green's function in the conformal normal coordinates. Finally, we give some application in section 4. This report is based on the lecture note by R. Schoen and S.-T. Yau and the paper by J. M. Lee and T. H. Parker.
[1] Alfred Gray, The volume of a small geodesic ball of a Riemannian manifold, Michigan Math. J. 20 (1973), 329-344
[2] John M. Lee and Thomas H. Parker, The Yamabe problem, Bull. Amer.Math. Soc. 17 (1987), 37-91
[3] R. Schoen and S.-T. Yau, Lectures on Differential Geometry, International Press, Boston 1994.
[4] A. Z. Petrov, Einstein spaces, translated by R. F. Kelleher, Pergamon Press, New York, 1969.
[5] L. P. Eisenhart, Riemannian geometry, Princeton Univ. Press, Princeton, N.J., 1949.
[6] Carmo, M. do, Riemannian geometry, translated by F. Flaherty, Birkhauser, Boston, 1992.
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