正質量定理的相關研究

A Survey on Positive Mass Theorem

王業凱(Ye-Kai Wang)

指導教授 ： 李瑩英

國立臺灣大學/理學院/數學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.01892

摘要

這篇文章介紹 quasilocal mass 的相關研究，主要是 Brown-York and Liu-Yau quasilocal mass 的定義以及如何證明它們是非負的。第一個重要發現是史宇光與譚聯輝證明了 time-symmetric 的情形，接著劉秋菊與丘成桐給出一般情形下的證明，最後我們討論王慕道與丘成桐最近提出的 quasilocal mass 的定義。

關鍵字

正質量定理

並列摘要

This note surveys the definition of quasilocal mass and its positivity. In particular, we focus on Brown-York and Liu-Yau quasilocal mass. We first present Shi and Tam's result on the positivity of quasilocal mass in the Riemannian case and then Liu and Yau's approach to the general case. Finally, we mention a modification of Liu-Yau quasilocal mass by Wang and Yau.

並列關鍵字

quasilocal mass ； positive mass theorem ； quasi-spherical ； isometric embedding ； static mean curvature

參考文獻

[B] Bartnik, Robert The mass of an asymptotically flat manifold. Comm. Pure Appl.

[CY] Christodoulou, D.; Yau, S.-T. Some remarks on the quasi-local mass. Mathematics

[Epp] Epp, Richard J. Angular momentum and an invariant quasilocal energy in general

relativity. Phys. Rev. D (3) 62 (2000), no. 12, 124108

[LY1] Liu, Chiu-Chu Melissa; Yau, Shing-Tung Positivity of quasilocal mass. Phys.