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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/43123完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 李瑩英 | |
| dc.contributor.author | Jui-En Chang | en |
| dc.contributor.author | 張瑞恩 | zh_TW |
| dc.date.accessioned | 2021-06-15T01:38:06Z | - |
| dc.date.available | 2010-07-17 | |
| dc.date.copyright | 2009-07-17 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-07-16 | |
| dc.identifier.citation | [1] R. M. Schoen and S.-T. Yau, Lectures on Differential Geometry, 1994, International
Press [2] Simon Brendle, On the conformal scalar curvature equation and related problems, arXiv: 0802.0295v1 [3] R. M. Schoen, Cyclic Coverings, Calabi-Yau Manifolds, and Complex multiplication, Ch. Vatiational Theory for the Total Scalar Curvature Functional for Riemannian Metrics and Related Topics, p120~154 [4] John M. Lee and Thomas H. Parker, The Yamabe Problem, BULLETN OF THE AMERICAN MATHEMATICAL SOCIETY, volume 17, Number 1, July 1987, p.31~p.91 [5] Rugang Ye, Global Existence and Convergence of Yamabe Flow, J. DIFFERENTIAL GEOMETRY, Volume 39, 1994, p.35~50 [6] Simon Brendle, Convergence of the Yamabe Flow for Arbitrary Initial Energy, U. DIFFERENTIAL GEOMETRY, Volume 69, 2005, p.217~278 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/43123 | - |
| dc.description.abstract | Yamabe問題內容如下：給定任何一個三維以上的黎曼緊緻流形，找一個保角的度量使得在此度量之下的純量曲率為一定值。此問題已經被Richard Schoen 在 1984 年完全解決。本論文研究此問題的證明。並且對於此問題的拋物偏微分方程版本， Yamabe 流，在本論文中也收錄了一些相關的結果。 | zh_TW |
| dc.description.abstract | The Yamabe problem is as following. Given a compact Riemannian manifold of dimension n≥3, find a conformal metric with constant scalar curvature. The problem is completely solved by Richard Schoen in 1984. This thesis studies the proof of the Yamabe problem. It also includes some results of the Yamabe flow, which is the parabolic counterpart of the Yamabe problem. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T01:38:06Z (GMT). No. of bitstreams: 1 ntu-98-R96221002-1.pdf: 669349 bytes, checksum: 8c6e24d39387a9163fdcdab9ce0b02ce (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | Contents
致謝 ii 中文摘要 iii 英文摘要 iii 1 Introduction 1 2 The P.D.E and the scalar curvature functional 4 2.1 Derive the P.D.E. for the Yamabe problem 4 2.2 The scalar curvarure functional 8 3 The proof of Yamabe problem 14 3.1 The best constant of Sobolev inequality 15 3.2 Relation between lambda(M) and the solution of the Yamabe problem 17 3.3 Construction of the conformal normal coordinate 22 3.4 The asymptotic expansion of the Green function of the conformal Laplacian operator 28 3.5 Construction of the test function on the asymptotically flat manifold 35 3.6 Positive mass theorem and the complete solution of the Yamabe problem 42 4 Use Yamabe flow to solve Yamabe problem 44 4.1 The long time existence 45 4.2 The case that lambda(M) is non-positive 46 4.3 The case when 3 ≤ dim(M) ≤ 5 or M is locally conformally flat 47 4.4 The other cases 49 References 50 | |
| dc.language.iso | zh-TW | |
| dc.title | Yamabe problem 的相關研究 | zh_TW |
| dc.title | Survey on Yamabe problem | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 王藹農,張樹城,鄭日新 | |
| dc.subject.keyword | 保角變換,純量曲率,Yamabe 問題, | zh_TW |
| dc.subject.keyword | conformal diffeomorphism,scalar curvature,Yamabe problem, | en |
| dc.relation.page | 50 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2009-07-16 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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