請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/7931完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 張樹城(Shu-Cheng Chang) | |
| dc.contributor.author | Tsung-Wei Hu | en |
| dc.contributor.author | 胡宗維 | zh_TW |
| dc.date.accessioned | 2021-05-19T17:59:10Z | - |
| dc.date.available | 2021-08-02 | |
| dc.date.available | 2021-05-19T17:59:10Z | - |
| dc.date.copyright | 2016-08-02 | |
| dc.date.issued | 2016 | |
| dc.date.submitted | 2016-07-27 | |
| dc.identifier.citation | [1] O. Munteanu and J. P. Wang , Geometry of shrinking Ricci solitons. Compositio Mathematica, 151, 2273-2300 (2015)
[2] H. D. Cao and D. Zhou, On complete gradient shrinking Ricci solitons, J. Diff. Geom.85, no. 2, 175-186 (2010) [3] B. L. Chen, Stron uniqueness of the Ricci flow, J. Diff. Geom. 82, no. 2,362-382 (2009) [4] B. Chow, R. Lu and B. Yang, A lower bound for the scalar curvature of noncompact nonflat Ricci shrinkers, Comptes Rendus Mathematique. 349, no. 23-24, 1265-1267 (2011) [5] J. Enders, R. Müller, P. Topping, On Type-I singularities in Ricci Flow, Comm. Anal. Geom. 19, , no. 5, 905-922 (2011) [6] P. Petersen and W. Wylie, On the classification of gradient Ricci solitons, Geom. Topol. 14, ,2277-2300 (2010) | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/7931 | - |
| dc.description.abstract | 瑞曲流(Ricci flow) 為理察• 哈密頓(Richard Hamilton) 為解決三維龐加萊猜想(Poincaré conjecture) 所發展的重要工具。瑞曲流中的孤立子(Solitons) 是在瑞曲流中的自我相似解(self-similar solution)，是瑞曲流奇點的重要模型，裴瑞爾曼(Grigori Perelman) 在三維成功發展處理孤立子的技巧，進而解決龐加萊猜想。這些孤立子的分類中，有一類稱為梯度孤立子(Gradient soliton)，可由梯度函數描述。
在2015 年Ovidiu Munteanu 與王嘉平共同發表的一篇論文中，展示了一種估計四維瑞曲流梯度孤立子中黎曼曲率、里奇曲率與純量曲率的方法，本論文將介紹前人在多維度梯度孤立子的一些結果，並介紹Ovidiu Munteanu 與王嘉平在四維上的估計方法。 | zh_TW |
| dc.description.abstract | To solve the Poincaré conjecture on 3-dimensional cases, Richard Hamilton evolved an algorithm called Ricci flow. In Ricci flow, a class of self-similar solutions called gradient solitons. Studing of such kink solution is playing an important role in solving Poincaré conjecture.
In 2015, Ovidiu Munteanu and Jiaping Wang shown an algorithm to estimate the Riemann, Ricci curvature and scalar curvature on 4-dimansional gradient solitons in Ricci flow. In this survey, I would introduce some early results in gradient solitons and explore the details in Ovidiu Munteanu and Jiaping Wang’s paper in 4-dimensional shrinking solitons. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-19T17:59:10Z (GMT). No. of bitstreams: 1 ntu-105-R03221006-1.pdf: 371442 bytes, checksum: a44b218fcdfa2d0d0fa32b07f2681254 (MD5) Previous issue date: 2016 | en |
| dc.description.tableofcontents | 致謝 i
中文摘要 ii 英文摘要 iii 1 Introduction 1 2 Preliminary Results in Gradient Ricci Solotion 2 3 Maximum principle on shrinking gradient Ricci solitons 4 4 Constant Upper bound of Curvature 8 5 Curvature Bounded by Scalar curvature 12 6 Curevature lower bound 17 參考文獻 20 | |
| dc.language.iso | en | |
| dc.title | 瑞曲流孤立子 | zh_TW |
| dc.title | A Survey on Gradient Ricci Solitons | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 崔茂培(Mao-Pei Tsui),吳進通(Chin-Tung Wu) | |
| dc.subject.keyword | 瑞曲流,孤立子, | zh_TW |
| dc.subject.keyword | Ricci flow,Soliton, | en |
| dc.relation.page | 20 | |
| dc.identifier.doi | 10.6342/NTU201601353 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2016-07-27 | |
| 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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