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作者(中文):李吉翔
作者(外文):Lee, Ji Shiang
論文名稱(中文):完備流形上的體積比較定理
論文名稱(外文):A note on volume comparison theorem on smooth metric measure space
指導教授(中文):宋瓊珠
指導教授(外文):Sung, Chiung Jue
口試委員(中文):高淑蓉
王嘉平
學位類別:碩士
校院名稱:國立清華大學
系所名稱:數學系
學號:102021509
出版年(民國):104
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 theoremsmooth metric measure space
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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.
1. Introduction - 3
2. Preliminaries - 6
3. Volume comparion on the complete Riemannian manifold -20
4. Volume upper bound - 23
5. Volume lower bound - 29
References - 37
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38 A NOTE ON VOLUME COMPARISON THEOREM ON SMOOTH METRIC MEASURE SPACE
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A NOTE ON VOLUME COMPARISON THEOREM ON SMOOTH METRIC MEASURE SPACE 39
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