完備流形上的體積比較定理

A note on volume comparison theorem on smooth metric measure space

李吉翔(Lee, Ji Shiang)

指導教授 ： 宋瓊珠

國立清華大學/理學院/數學系/碩士(2015年)

摘要

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。

關鍵字

完備流形 ； 體積比較定理

並列摘要

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.

並列關鍵字

volume comparison theorem ； smooth metric measure space

參考文獻

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