請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/2338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 | Yi-Lin Tsai | en |
| dc.contributor.author | 蔡宜霖 | zh_TW |
| dc.date.accessioned | 2021-05-13T06:39:16Z | - |
| dc.date.available | 2017-08-25 | |
| dc.date.available | 2021-05-13T06:39:16Z | - |
| dc.date.copyright | 2017-08-25 | |
| dc.date.issued | 2017 | |
| dc.date.submitted | 2017-08-15 | |
| dc.identifier.citation | [1] Charles Fefferman. Conformal invariants. Astérisque, (Numéro Hors Série):95–116. The mathematical heritage of Élie Cartan (Lyon, 1984).
[2] John G. Ratcliffe. Foundations of hyperbolic manifolds, volume 149 of Graduate Texts in Mathematics. Springer, New York, 2 edition. [3] C. Robin Graham. Volume and area renormalizations for conformally compact einstein metrics. Rend. Circ. Mat. Palermo (2) Suppl., (63):31–42. [4] C. Robin Graham. Conformally invariant powers of the laplacian. i. existence. J.London Math. Soc.(2),46(3):557–565. [5] C. Robin Graham. Scattering matrix in conformal geometry. Invent. Math., 152(1):89–118. [6] Charles Fefferman. q-curvature and poincaré metrics. Math. Res. Lett., 9(2-3):139–151. [7] Rafe Mazzeo. The hodge cohomology of a conformally compact metric. J. Differ-ential Geom., 28(2):309–339. [8] C. Robin Graham. Einstein metrics with prescribed conformal infinity on the ball.Adv. Math., 87(2):186–225. [9] Jacques Lafontaine. Conformal geometry from the riemannian viewpoint. pages65–92. [10] Fritz John. Partial differential equations, volume 1 of Applied Mathematical Sciences. Springer-Verlag, New York, 4 edition. [11] Vijay Balasubramanian. A stress tensor for anti-de sitter gravity. Comm. Math. Phys.,208(2):413–428. [12] A Gover and Andrew Waldron. Renormalized volume. arXiv preprint arXiv:1603.07367, 2016. [13] S. J. Patterson. The divisor of Selberg’s zeta function for Kleinian groups, volume 106. Appendix A by Charles Epstein. [14] Sean Curry and A Gover. An introduction to conformal geometry and tractor calculus, with a view to applications in general relativity. arXiv preprint arXiv:1412.7559,2014. [15] Stephen M. Paneitz. A quartic conformally covariant differential operator for arbitrary pseudo-riemannian manifolds (summary). SIGMA Symmetry Integrability Geom. Methods Appl., 4:Paper 036, 3. [16] Thomas P. Branson. Explicit functional determinants in four dimensions. Proc.Amer. Math. Soc., 113(3):669–682. [17] N. H. Kuiper. On conformally-flat spaces in the large. Ann. of Math. (2), 50:916–924. [18] Richard B. Melrose. Geometric scattering theory. Stanford Lectures. Cambridge University Press, Cambridge. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/2338 | - |
| dc.description.abstract | 在這篇文章裡，我探討了保角緊緻流形的重要結果及其關聯性。這些主題包含了重整化體積，GJMS算子，Q曲率和基礎的散射理論。這篇文章的主旨是從不同的歷史發展出發來看保角緊緻流形的研究，並探討這些不同的歷史發展交匯時的結果。 | zh_TW |
| dc.description.abstract | In this paper, I survey several important results for conformally compact manifolds and relate these different objects together. These topics includes renormalized volume, GJMS operators, Q-curvature, and basic scattering theory. The main goal of this paper is to survey conformally compact manifolds from different historical developments and discuss how these developments are related. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-13T06:39:16Z (GMT). No. of bitstreams: 1 ntu-106-R03221034-1.pdf: 434690 bytes, checksum: 9e3a2424603a15b607f40d8841eb93a5 (MD5) Previous issue date: 2017 | en |
| dc.description.tableofcontents | 1 Introduction ...............................1
2 Basic properties ...........................4 3 Renormalized volume ........................7 4 GJMS operators and scattering theory ......12 4.1 GJMS operators ..........................12 4.2 Scattering theory .......................18 5 Application ...............................22 Bibliography ................................26 | |
| dc.language.iso | en | |
| dc.subject | 保角緊緻流形 | zh_TW |
| dc.subject | conformally compact manifolds | en |
| dc.title | 保角緊緻流形之相關探討 | zh_TW |
| dc.title | A survey on conformally compact manifolds | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 105-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 蔡忠潤(Chung-Jun Tsai),崔茂培(Mao-Pei Tsui),鄭日新(Jih-Hsin Cheng) | |
| dc.subject.keyword | 保角緊緻流形, | zh_TW |
| dc.subject.keyword | conformally compact manifolds, | en |
| dc.relation.page | 27 | |
| dc.identifier.doi | 10.6342/NTU201703321 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2017-08-15 | |
| 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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