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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 崔茂培(Mao-Pei Tsui) | |
| dc.contributor.author | Jin-Han Liou | en |
| dc.contributor.author | 劉晉翰 | zh_TW |
| dc.date.accessioned | 2021-05-13T08:36:11Z | - |
| dc.date.available | 2016-08-26 | |
| dc.date.available | 2021-05-13T08:36:11Z | - |
| dc.date.copyright | 2016-08-26 | |
| dc.date.issued | 2016 | |
| dc.date.submitted | 2016-08-17 | |
| dc.identifier.citation | 1. 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. 8. C. Misner, K. Thorne and J. Wheeler, Gravitation, W. H. Freeman (1973). MR 0418833. 9. N. Ó Murchadha, L.B. Szabados and K.P. Tod, Comment on 'Positivity of quasilocal mass', Phys. Rev. Lett. 92, 259001 (2004). Zbl 1267.83029. http://dx.doi.org/10.1103/PhysRevLett.92.259001. 10. L. Nirenberg, The Weyl and Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math. 6 (1953), 337-394. MR 0058265. Zbl 0051.12402. http://dx.doi.org/10.1002/cpa.3160060303. 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. 15. R. Schoen and S.-T. Yau, Proof of the positive mass theorem. II, Comm. Math. Phys. 79, 231 (1981), 231-260. MR 0612249. Zbl 0494.53028. http://dx.doi.org/10.1007/BF01942062. 16. Y. Shi and L.-F. Tam, Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature, J. Diff. Geo. 62 (2002), 79-125. MR 1987378. Zbl 1071.53018. http://arxiv.org/abs/math/0301047. 17. L. B. Szabados, Quasi-local energy-momentum and angular momentum in general relativity, Living Rev. Relativity 12 (2009). Zbl 1215.83010. http://dx.doi.org/10.12942/lrr-2009-4. 18. R. M. Wald, General relativity, Univ. Chicago Press, (1984). MR 0757180. Zbl 0549.53001. http://dx.doi.org/10.7208/chicago/9780226870373.001.0001. 19. M.-T. Wang, Four lectures on quasi-local mass, (2015). arXiv 1510.02931. 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. 21. M.-T. Wang and S.-T. Yau, Quasilocal mass in general relativity, Phys. Rev. Lett. 102 021101 (2009), no.2. MR 2475769. http://dx.doi.org/10.1103/PhysRevLett.102.021101. 22. E. Witten, A new proof of the positive energy theorem, Comm. Math. Phys. 80 (1981), 381-402. MR 0626707. Zbl 1051.83532. http://dx.doi.org/10.1007/BF01208277. 23. J. W. York, Boundary terms in the action principles of general relativity, Found. Phys. 16 (1986), 249-257. MR 0895491. http://dx.doi.org/10.1007/BF01889475. | |
| dc.identifier.uri | http://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.abstract | In 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.provenance | Made 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.iso | en | |
| dc.subject | 王-丘擬局部質量 | zh_TW |
| dc.subject | Wang-Yau quasi-local mass | en |
| dc.title | 王-丘擬局部質量之探討 | zh_TW |
| dc.title | A Note on Wang-Yau Quasi-Local Mass | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-2 | |
| 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.keyword | Wang-Yau quasi-local mass, | en |
| dc.relation.page | 26 | |
| dc.identifier.doi | 10.6342/NTU201602493 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2016-08-17 | |
| 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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