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  1. NTU Theses and Dissertations Repository
  2. 理學院
  3. 數學系
請用此 Handle URI 來引用此文件: http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/3719
完整後設資料紀錄
DC 欄位值語言
dc.contributor.advisor崔茂培(Mao-Pei Tsui)
dc.contributor.authorJin-Han Liouen
dc.contributor.author劉晉翰zh_TW
dc.date.accessioned2021-05-13T08:36:11Z-
dc.date.available2016-08-26
dc.date.available2021-05-13T08:36:11Z-
dc.date.copyright2016-08-26
dc.date.issued2016
dc.date.submitted2016-08-17
dc.identifier.citation1. H. Bondi, M. G. J. van der Burg and A. W. K. Metzner, Gravitational waves in general relativity. VII. Waves from axi-symmetric isolated systems, Proc. Roy. Soc. A 269 (1962). MR 0147276. Zbl 0106.41903. http://dx.doi.org/10.1098/rspa.1962.0161.
2. J. D. Brown and J. W. York, Quasilocal energy in general relativity, in Mathematical aspects of classical field theory (Seattle, WA, 1991), Contemp. Math. 132 (1992), 129-142. MR 1188439. Zbl 0784.53039. http://dx.doi.org/10.1090/conm/132/1188439.
3. J. D. Brown and J. W. York, Quasilocal energy and conserved charges derived from the gravitational action, Phys. Rev. D (3) 47(4) (1993), 1407-1419. MR 1211109. http://dx.doi.org/10.1103/PhysRevD.47.1407.
4. S. W. Hawking and G. F. R. Ellis, The large scale structure of space-time, Cambridge Univ. Press, (1973). MR 0424186. Zbl 0265.53054. http://dx.doi.org/10.1017/CBO9780511524646.
5. P. S. Jang, On the positivity of energy in general relativity, J. Math. Phys. 19(5), (1978), 1152-1155. http://dx.doi.org/10.1063/1.523776.
6. C.-C.M. Liu and S.-T. Yau, Positivity of quasilocal mass, Phys. Rev. Lett. 90(23), 231102 (2003). MR 2000281. Zbl 1267.83028. http://arxiv.org/abs/gr-qc/0303019.
7. C.-C.M. Liu and S.-T. Yau, Positivity of quasi-local mass II, J. Amer. Math. Soc. 19(1) (2006), 181-204. MR 2169046. Zbl 1081.83008. http://arxiv.org/abs/math/0412292.
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11. R. Penrose, Some unsolved problems in classical general relativity, Seminar on Differential Geometry, Ann. of Math. Stud., 102, Princeton Univ. Press, Princeton, N.J. (1982), 631-668. MR 0645761. Zbl 0481.53053. http://dx.doi.org/10.1515/9781400881918-034.
12. A. Pogorelov, Regularity of a convex surface with given Gaussian curvature, Mat. Sb. (N.S.) 31(73) (1952), 88-103. MR 0052807. Zbl 0048.40501.
13. R. K. Sachs, Gravitational waves in general relativity. VIII. Waves in asymptotically flat space-time, Proc. Roy. Soc. A, 270 (1962). MR 0149908. Zbl 0101.43605. http://dx.doi.org/10.1098/rspa.1962.0206.
14. R. Schoen and S.-T. Yau, On the proof of the positive mass conjecture in general relativity, Comm. Math. Phys. 65, (1979), 45-76. MR 0526976. Zbl 0405.53045. http://dx.doi.org/10.1007/BF01940959.
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20. M.-T. Wang and S.-T. Yau, Isometric embeddings into the Minkowski space and new quasi-local mass, Comm. Math. Phys. 288 (2009), 919-942. MR 2504860. Zbl 1195.53039. http://dx.doi.org/10.1007/s00220-009-0745-0.
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dc.identifier.urihttp://tdr.lib.ntu.edu.tw/jspui/handle/123456789/3719-
dc.description.abstract本文回顧王-丘擬局部質量之物理背景與數學建構。最後在第三章討論王-丘擬局部質量之非負特性。zh_TW
dc.description.abstractIn this master thesis, we review the notion about the Wang-Yau quasi-local mass from the physical background to the mathematical construction. Finally, we discuss the positivity argument of Wang-Yau quasi-local mass in Wang-Yau's original paper.en
dc.description.provenanceMade available in DSpace on 2021-05-13T08:36:11Z (GMT). No. of bitstreams: 1
ntu-105-R03221011-1.pdf: 532436 bytes, checksum: 60d3e5d083e96a545bb4b26ed32f53ae (MD5)
Previous issue date: 2016
en
dc.description.tableofcontents致謝 i
摘要 ii
Abstract iii
1 Introduction 1
2 Preliminary 4
2.1 Notations 4
2.2 Constraint equations and dominant energy condition 5
2.3 Action principle 6
2.4 Hamiltonian formulation 9
3 Wang-Yau Quasi-Local Mass 14
3.1 The definition 14
3.2 Jang-Schoen-Yau equation 20
3.3 Shi-Tam inequality 22
3.4 The positivity 22
Bibliography 24
dc.language.isoen
dc.subject王-丘擬局部質量zh_TW
dc.subjectWang-Yau quasi-local massen
dc.title王-丘擬局部質量之探討zh_TW
dc.titleA Note on Wang-Yau Quasi-Local Massen
dc.typeThesis
dc.date.schoolyear104-2
dc.description.degree碩士
dc.contributor.oralexamcommittee王慕道(Mu-Tao Wang),蔡忠潤(Chung-Jun Tsai),李瑩英(Yng-Ing Lee)
dc.subject.keyword王-丘擬局部質量,zh_TW
dc.subject.keywordWang-Yau quasi-local mass,en
dc.relation.page26
dc.identifier.doi10.6342/NTU201602493
dc.rights.note同意授權(全球公開)
dc.date.accepted2016-08-17
dc.contributor.author-college理學院zh_TW
dc.contributor.author-dept數學研究所zh_TW
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