在三維度柯西黎曼流行上的仿埃米爾特質量變分公式

The variation of p-mass on three dimensional CR manifolds

高尉庭(Wei-Ting Kao)

指導教授 ： 鄭日新

國立臺灣大學/理學院/數學研究所/碩士(2018年)

https://doi.org/10.6342/NTU201802485

摘要

我們考慮用一函數定義的一簇仿埃爾米特流型在二維複向量空間，並在這擾動下給出仿埃爾米特質量的變分公式。為了得出這個結果，我們推廣了Graham 跟Lee所導出的環繞聯絡使其可應用在任意的切觸形式對於這簇仿埃爾米特流型，並且導出在這理論下的共形變換公式去得到偽質量的變分公式。

關鍵字

柯西黎曼流型 ； 正質量定理

並列摘要

We consider a family of pseudohermitian manifolds in two dimensional complex vector space, described by the level sets of a defining function, and give the variation formula of p-mass for this deformation. To obtain this result, we generalize the ambient connection done by Graham and Lee for arbitrary contact form and derive the conformal transformation in this theory.

並列關鍵字

pseudohermitian manifold ； pseudohermitian mass ； positive mass theorem

參考文獻

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[5] C Robin Graham, John M Lee, et al. Smooth solutions of degenerate laplacians on strictly pseudoconvex domains. Duke mathematical journal, 57(3):697–720, 1988.