| 姓名 |
賴馨華(Sin-hua Lai)
查詢紙本館藏 |
畢業系所 |
數學系 |
| 論文名稱 |
沿著瑞奇流的κ-noncollapsing 估計
(κ－Noncollapsing estimates along the Ricci flow)
|
| 相關論文 | |
| 檔案 |
 [Endnote RIS 格式]
[Bibtex 格式]
 [相關文章]  [文章引用]  [完整記錄]  [館藏目錄]  [檢視] [下載]- 本電子論文使用權限為同意立即開放。
- 已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
- 請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。
|
| 摘要(中) |
在這篇文章裡我們描述了兩種由Perelman提出建立沿著瑞奇
流的κ-noncollapsing定理的方法。第一種方法是使用Perelman entropy。第二種方法是利用Perelman’s reduced volume的單調性來建立。Reduced volume是對non-collapsing定理更局部的看法，因此我們學習Perelman的証明中關於龐加萊猜想裡ancient κ-noncollapsing的解時(這種解不必是緊緻因此不被總體的量所控制)，第二個方法是重要的。我們的論述主要是依據Cao-Zhu [6]，關於Perelman’s Wfunctional我們參考O. Rothaus [3]給予更詳細的說明。 |
| 摘要(英) |
In this paper we report on the two methods pioneered by G. Perelman[1] to establish his κ-noncollapsing thm of the Ricci flow. The first method uses the Perelman entropy. The second proof uses the monotonicity of the Perelman’s reduced volume. The second proof is important, because the reduced volume is a more localized quantity in its definition and so one can in fact establish local versions
of the non-collapsing theorem which turn out to be important when we study ancient κ-noncollapsing solutions in Perelman’s proof of the Poincar´e conjecture. Such solutions need not be compact and so cannot be controlled by global quantities (such as the Perelman entropy). Our treatment follows closely the cuticle by Cao-Zhu [6],
with some more details on Perelman’s W functional by O. Rothaus [3]. |
| 關鍵字(中) |
★ 沿著瑞奇流的κ-noncollapsing 估計 |
關鍵字(英) |
★ κ－Noncollapsing estimates along the Ricci flow |
| 論文目次 |
中文摘要................................................i
英文摘要...............................................ii
Contents..............................................iii
1.Introduction........................................p.2
2. Perelman’s Reduce Volume .........................p.4
3. No local collapsing theorem.......................p.11
References...........................................p.20 |
| 參考文獻 |
[1] G PERELMANN ”The entropy formula for the Ricci flow and its geometric applications”, arXiv:math. DG/0211159 v1 November 11,2002, preprint.
[2] BRUCE KLEINER AND JOHN LOTT, ”Notes on Perelman’s Papers”, arXive: math/0605667v2 [math.DG] 21 Feb 2007
[3] O.ROTHAUS, ”Logarithmic Sobolev Inequalities and the Spectrum of Schr¨odinger Operators”, J. Funct. Anal. 42, p. 110-120(1981)
[4] J. CHEEGER AND D. EBIN, ”Comparison thorems in Riemannian geometry”, North-Holland,1975.
[5] R. SCHOEN AND S.-T. YAU, ”Lectures on differential geometry, in Conference Proceedings and Lecture Notes in Geometry and Topology”,1, International Press Publications, 1994.
[6] HUAI-DONG CAO AND XI-PING ZHU,”A complete proof of the Poincar´e and geometrization conjectures-application of the Hamilton-Perelman theory of
the Ricci flow” Asian J.Math. Vol. 10, No. 2, pp. 165-492, June 2006. |
| 指導教授 |
王金龍(Chin-lung Wang)
|
審核日期 |
2008-7-14 |
| 推文 |
 facebook  plurk  twitter  funp  google  live  udn  HD  myshare  reddit  netvibes  friend  youpush  delicious  baidu
|
| 網路書籤 |
 Google bookmarks  del.icio.us  hemidemi myshare
|
