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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/91639完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 王藹農 | zh_TW |
| dc.contributor.advisor | Ai-Nung Wang | en |
| dc.contributor.author | 簡培育 | zh_TW |
| dc.contributor.author | Pei-Yu Jian | en |
| dc.date.accessioned | 2024-02-20T16:20:05Z | - |
| dc.date.available | 2024-02-21 | - |
| dc.date.copyright | 2024-02-20 | - |
| dc.date.issued | 2024 | - |
| dc.date.submitted | 2024-01-26 | - |
| dc.identifier.citation | [1] Ben Andrews, Bennett Chow, Christine Guenther, and Mat Langford, Extrinsic geometric flows, Graduate Studies in Mathematics, Vol. 206, American Mathematical Society, Providence, Rhode Island, 2020.
[2] D. Christodoulou and S.-T. Yau, Some remarks on the quasi-local mass, in: James A. Isenberg, ed., Contemporary Mathematics, Vol. 71, Proceedings of the AMS-IMS-SIAM joint summer research conference, June 22-28, 1986, American Mathematical Society, Providence, Rhode Island, 1988, 9-14. [3] Douglas M. Eardley, Global problems in numerical relativity, in: Larry L. Smarr, ed., Sources of gravitational radiation, Proceedings of the Battelle Seattle workshop, July 27 - August 4, 1978, Cambridge University Press, Cambridge, 1979, 127-138. [4] Robert Geroch, Energy extraction, Ann. N. Y. Acad. Sci. 224 (1973), no. 1, 108-117, DOI 10.1111/j.1749-6632.1973.tb41445.x. [5] S. W. Hawking, Gravitational radiation in an expanding universe, J. Math. Phys. 9 (1968), no. 4, 598-604, DOI 10.1063/1.1664615. [6] Gerhard Huisken and Alexander Polden, Geometric evolution equations for hypersurfaces, in: Stefan Hildebrandt and Michael Struwe, eds., Lecture Notes in Mathematics, Vol. 1713, Lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetaro, Italy, June 15-22, 1996, Springer-Verlag, Heidelberg, 1999, 45-84, DOI 10.1007/BFb0092669. [7] Gerhard Huisken and Tom Ilmanen, The Riemannian Penrose inequality, Int. Math. Res. Not. 1997 (1997), no. 20, 1045-1058, DOI 10.1155/S1073792897000664 [8] Gerhard Huisken and Tom Ilmanen, The inverse mean curvature flow and the Riemannian Penrose inequality, J. Differential Geom. 59 (2001), no. 3, 353-437, DOI 10.4310/jdg/1090349447. [9] Sven Hirsch, Hawking mass monotonicity for initial data sets, arXiv:2210.12237v2 [math.DG], 2023. [10] John M. Lee, Introduction to Riemannian manifolds, 2nd ed., Graduate Texts in Mathematics, Vol. 176, Springer, Cham, 2018, DOI 10.1007/978-3-319-91755-9. [11] Dan A. Lee, Geometric relativity, Graduate Studies in Mathematics, Vol. 201, American Mathematical Society, Providence, Rhode Island, 2019. [12] Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler, Gravitation, Princeton University Press, Princeton and Oxford, 2017. Reprint of the 1973 original. [13] László B. Szabados, Quasi-local energy-momentum and angular momentum in general relativity, Living Rev. Relativ. 12 (2009), no. 4, DOI 10.12942/lrr-2009-4. [14] Oliver C. Schnürer, Geometric flow equations, in: Vicente Cortés, Klaus Kröncke, and Jan Louis, eds., Geometric flows and the geometry of space-time, Lectures given at the summer school held at the University of Hamburg, September 19-23, 2016, Birkhäuser, Cham, 2018, 77-121, DOI 10.1007/978-3-030-01126-0_2. [15] Robert M. Wald, General relativity, The University of Chicago Press, Chicago and London, 1984. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/91639 | - |
| dc.description.abstract | 廣義相對論中的霍金準局部能量為 S. W. Hawking 在1968年提出的概念，其在逆平均曲率流下的單調性以隱晦的方式初見於一篇1973年的文章，文章作者為 Robert Geroch ，因此該性質一般稱作傑勒西單調性公式。標誌著非負的時變率，這個公式在近代許多幾何流、數學相對論的文獻中被明白揭示並證明，其中一篇文獻是 Gerhard Huisken 與 Alexander Polden 在1996年完成的工作，此二人證明公式的手法為取得幾個演化方程後再求能量的時變率。在這份評注中，我們將詳述 Huisken 與 Polden 如何在那篇1996年的文章中證明傑勒西單調性公式。 | zh_TW |
| dc.description.abstract | The Hawking quasi-local energy in general relativity is a notion proposed by S. W. Hawking in 1968. Its monotonicity under inverse mean curvature flow was first suggested in a 1973 article authored by Robert Geroch, commonly known as the Geroch monotonicity formula. As a non-negative time derivative, this formula is explicitly stated and proved in many of the modern references on mathematical relativity and geometric flows, including an article composed by Gerhard Huisken and Alexander Polden in 1996. Huisken and Polden proved the formula by taking the time derivative of the energy function after some evolution equations were developed. In this note, we shall present a detailed exposition of how Huisken and Polden prove the Geroch monotonicity formula in the 1996 article. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-02-20T16:20:05Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2024-02-20T16:20:05Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Thesis acceptance certificate i
Acknowledgements ii Abstract in Chinese iii Abstract in English iv 1 Introduction 1 2 Preliminaries 5 3 Proof of the formula 13 4 Weak formulation 16 A The Gauss-Weingarten equations 18 B Mean curvature as divergence 20 Bibliography 22 | - |
| dc.language.iso | en | - |
| dc.subject | 準局部能量 | zh_TW |
| dc.subject | 霍金能量 | zh_TW |
| dc.subject | 幾何演化方程 | zh_TW |
| dc.subject | 逆平均曲率流 | zh_TW |
| dc.subject | 傑勒西單調性 | zh_TW |
| dc.subject | inverse mean curvature flow | en |
| dc.subject | quasi-local energy | en |
| dc.subject | Hawking energy | en |
| dc.subject | geometric evolution equation | en |
| dc.subject | Geroch monotonicity | en |
| dc.title | 一個關於傑勒西單調性公式的評注 | zh_TW |
| dc.title | A Note on the Geroch Monotonicity Formula | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 112-1 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 梁惠禎;張海潮 | zh_TW |
| dc.contributor.oralexamcommittee | Fei-tsen Liang;Hai-Chau Chang | en |
| dc.subject.keyword | 準局部能量,霍金能量,幾何演化方程,逆平均曲率流,傑勒西單調性, | zh_TW |
| dc.subject.keyword | quasi-local energy,Hawking energy,geometric evolution equation,inverse mean curvature flow,Geroch monotonicity, | en |
| dc.relation.page | 23 | - |
| dc.identifier.doi | 10.6342/NTU202400037 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2024-01-30 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 數學系 | - |
| 顯示於系所單位： | 數學系 | |
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