封閉曲面上拉普拉斯算子第一特徵值的最優上界

Sharp Upper Bounds of the First Eigenvalues of the Laplacian Operators on Closed Surfaces

趙凱衞(Kai-Wei Zhao)

指導教授 ： 李瑩英

國立臺灣大學/理學院/數學研究所/碩士(2014年)

https://doi.org/10.6342/NTU.2014.01293

摘要

本論文將統整一些在球面、投影實平面以及輪胎面上求得以面積表示的拉普拉斯算子第一特徵值最優上界之方法。

關鍵字

拉普拉斯算子 ； 特徵值問題 ； 譜幾何 ； 最優上界 ； 最優不等式

並列摘要

In this thesis, we will summarize some approaches to obtain sharp upper bounds of the first nonzero eigenvalues of the Laplacian operators on closed surfaces, including sphere S2, real projective plane RP2 and torus T2, in terms of their areas.

並列關鍵字

Laplacian operator ； eigenvalue problem ； spectrum geometry ； sharp upper bound ； sharp inequality

參考文獻

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