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| 研究生： |
陳義麟 Chen, Yi-Lin |
|---|---|
| 論文名稱： |
完備光滑可測度空間上的函數理論 The Function Theory on Complete Smooth Metric Measure Spaces |
| 指導教授： |
宋瓊珠
Sung, Chiung-Jue |
| 口試委員: |
高淑蓉
Kao, Shu-Jung 蕭育如 Syau, Yu-Ru |
| 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： | 2012 |
| 畢業學年度： | 100 |
| 語文別： | 英文 |
| 論文頁數： | 32 |
| 中文關鍵詞： | 拉普拉斯算子比較 、體積比較定理 、梯度估計 、分解定理 |
| 外文關鍵詞： | Laplcian comparison, volume comparison, Bakry-Emery Ricci curvature |
| 相關次數： | 點閱：1 下載：0 |
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在這篇論文我們先研讀在非負曲率光滑可測度空間上的函數的梯度估計。並利用這個梯度估計證明在幾何維方程中Liouville型的定理結果以及空間的分解定定理。
In this note, we introduce the gradient estimate on smooth metric measure spaces with nonnegative Bakry-\'Emery Ricci curvature. We also apply such estimate to prove Liouville type theorem and splitting theorem in geometric partial differential equations.
K. Brighton, A Liouville-Type for Smooth Metric Measrue Spaces, arXiv:1006.0751.
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F. Fang, X.-D. Li and Z. Zhang, Two Generalizations of Cheenger-Gromoll Splitting Theorem via Bakry-Emery Ricci Curvature, Annales de l'Institut Fourier, 59 no.2 (2009), 563-573.
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