研究生: |
李吉翔 Lee, Ji Shiang |
---|---|
論文名稱: |
完備流形上的體積比較定理 A note on volume comparison theorem on smooth metric measure space |
指導教授: |
宋瓊珠
Sung, Chiung Jue |
口試委員: |
高淑蓉
王嘉平 |
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: | 2015 |
畢業學年度: | 103 |
語文別: | 英文 |
論文頁數: | 39 |
中文關鍵詞: | 完備流形 、體積比較定理 |
外文關鍵詞: | volume comparison theorem, smooth metric measure space |
相關次數: | 點閱:3 下載:0 |
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我們介紹一個在Bakry-Emery曲率有下界的完備流形上,當weight function是線性的或是二次增長的情況下對於測地球的體積比較定理。
Let (Mn,g,e−fdv) be a smooth metric measure space with Bakry-´Emery
curvature bounded below, we introduce the volume comparison theorem on such man
ifold. If the weighted function is of linear growth or of quadratic growth, we study the
volume upper and lower bound estimate of a geodesic ball on M.
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