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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/9671完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 李瑩英(Yng-Ing Lee) | |
| dc.contributor.author | Ye-Kai Wang | en |
| dc.contributor.author | 王業凱 | zh_TW |
| dc.date.accessioned | 2021-05-20T20:34:43Z | - |
| dc.date.available | 2008-08-05 | |
| dc.date.available | 2021-05-20T20:34:43Z | - |
| dc.date.copyright | 2008-08-05 | |
| dc.date.issued | 2008 | |
| dc.date.submitted | 2008-07-29 | |
| dc.identifier.citation | [B] Bartnik, Robert The mass of an asymptotically flat manifold. Comm. Pure Appl.
Math. 39 (1986), no. 5, 661–693. [CY] Christodoulou, D.; Yau, S.-T. Some remarks on the quasi-local mass. Mathematics and general relativity (Santa Cruz, CA, 1986), 9–14, Contemp. Math., 71, Amer. Math. Soc., Providence, RI, 1988. [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. Rev. Lett. 90 (2003), no. 23, 231102 [LY2] Liu, Chiu-Chu Melissa; Yau, Shing-Tung Positivity of quasi-local mass. II. J. Amer. Math. Soc. 19 (2006), no. 1, 181–204 [M] N. ´O. Murchadha The Liu-Yau mass as a quasi-local energy in general relativity, arXiv:0706.1166 [MST] N. ´O. Murchadha; L. B. Szabados; K. P. Tod. Comment on: “Positivity of quasilocal mass” Phys. Rev. Lett. 92 (2004), no. 25, 259001 [Ni] Nirenberg, Louis The Weyl and Minkowski problems in differential geometry in the large. Comm. Pure Appl. Math. 6, (1953). 337–394. [Po] Pogorelov, A. V. Regularity of a convex surface with given Gaussian curvature. (Russian) Mat. Sbornik N.S. 31(73), (1952). 88–103 [PT] Parker, Thomas; Taubes, Clifford Henry On Witten’s proof of the positive energy theorem. Comm. Math. Phys. 84 (1982), no. 2, 223–238. [ST] Shi, Yuguang; Tam, Luen-Fai Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature. J. Differential Geom. 62 (2002), no. 1, 79–125. [SY1] Schoen, Richard; Yau, Shing-Tung. On the proof of the positive mass conjecture in general relativity. Comm. Math. Phys. 65 (1979), no. 1, 45–76. [SY2] Schoen, Richard; Yau, Shing-Tung. Proof of the positive mass theorem. II. Comm. Math. Phys. 79 (1981), no. 2, 231–260. [Sz] L. B. Szabados. Quasi-local energy-momentum and angular momentum in GR: a review article Living Rev. Relativity, 7 (2004), 4. [W] Witten, Edward A new proof of the positive energy theorem. Comm. Math. Phys. 80 (1981), no. 3, 381–402. [WY] Wang, Mu-Tao; Yau, Shing-Tung. Isometric embedding into the Minkowski space and new quasi-local mass, arXiv:0805.1370v2 [Y] Yau, Shing-Tung. Geometry of three manifolds and existence of black hole due to boundary effect. Adv. Theor. Math. Phys. 5 (2001), no. 4, 755–767 16 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/9671 | - |
| dc.description.abstract | 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。 | zh_TW |
| dc.description.abstract | 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. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-20T20:34:43Z (GMT). No. of bitstreams: 1 ntu-97-R95221032-1.pdf: 451692 bytes, checksum: 6426f437640e3970871bb829fb234a1f (MD5) Previous issue date: 2008 | en |
| dc.description.tableofcontents | Contents
1 Introduction 1 2 The definition of Brown-York and Liu-Yau quasilocal mass 4 3 The Riemannian Case 5 4 The General Case 8 5 A new quasilocal mass of Wang and Yau 11 | |
| dc.language.iso | en | |
| dc.title | 正質量定理的相關研究 | zh_TW |
| dc.title | A Survey on Positive Mass Theorem | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 96-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 王藹農(Ai-Nung Wang),張樹城 | |
| dc.subject.keyword | 正質量定理, | zh_TW |
| dc.subject.keyword | quasilocal mass,positive mass theorem,quasi-spherical,isometric embedding,static mean curvature, | en |
| dc.relation.page | 15 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2008-07-30 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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