請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/4575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.author | Pang-Yen Chen | en |
| dc.contributor.author | 陳邦彥 | zh_TW |
| dc.date.accessioned | 2021-05-14T17:43:36Z | - |
| dc.date.available | 2016-02-02 | |
| dc.date.available | 2021-05-14T17:43:36Z | - |
| dc.date.copyright | 2016-02-02 | |
| dc.date.issued | 2015 | |
| dc.date.submitted | 2015-12-03 | |
| dc.identifier.citation | [1] Ben Andrews, Fully nonlinear parabolic equations in two space variables, preprint, available at
http://arxiv.org/pdf/math/0402235. [2] Qi Ding, The inverse mean curvature ow in rotationally symmetric spaces, Chin. Ann. Math. Ser. B 32 (2011), no. 1, 27{44. MR2772224 (2012d:53214). [3] Claus Gerhardt, Flow of nonconvex hypersurfaces into spheres, J. Di erential Geom. 32 (1990), no. 1, 299{314. MR1064876 (91k:53016). [4] Robert Geroch, Energy extraction, Annals of the New York Academy of Sciences 224 (1973), 108{117. [5] Pengfei Guan and Junfang Li, The quermassintegral inequalities for k-convex starshaped domains, Adv. Math. 221 (2009), no. 5, 1725{1732. MR2522433 (2010i:52021). [6] Richard S. Hamilton, Three-manifolds with positive Ricci curvature, J. Di erential Geom. 17 (1982), no. 2, 255{306. MR664497 (84a:53050). [7] Gerhard Huisken and Tom Ilmanen, The inverse mean curvature ow and the Riemannian Penrose inequality, J. Di erential Geom. 59 (2001), no. 3, 353{437. MR1916951 (2003h:53091). [8] Gerhard Huisken and Tom Ilmanen, Higher regularity of the inverse mean curvature ow, J. Di erential Geom. 80 (2008), no. 3, 433{451. MR2472479 (2010c:53097). [9] Pong Soo Jang and Robert M. Wald, The positive energy conjecture and the cosmic censor hypothesis, J. Mathematical Phys. 18 (1977), no. 1, 41{44. MR0523907 (58 no.25755). [10] N. V. Krylov, Boundedly inhomogeneous elliptic and parabolic equations, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), no. 3, 487{523, 670. MR661144 (84a:35091). [11] Haizhong Li and Yong Wei, On inverse mean curvature ow in Schwarzschild space and Kottler space, preprint, available at http://arxiv.org/pdf/1212.4218.pdf.. [12] John I. E. Urbas, On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures, Math. Z. 205 (1990), no. 3, 355{372. MR1082861 (92c:53037). | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/4575 | - |
| dc.description.abstract | 這篇文章中，我們討論超曲面在對曲率做合理假設下的旋轉對稱空間中沿著逆平均曲率流之行為。我們針對逆平均曲率流的初始曲面為封閉、星形且mean-convex之情形的長時間存在性以及近似行為做細部分析。另外我們利用逆平均曲率流來證明歐氏空間中定義域為星形且mean-convex之quermassintegrals的isoperimetric不等式。 | zh_TW |
| dc.description.abstract | In this thesis, we study the behavior of the motion of hypersurfaces by their inverse mean curvature flow (abbreviated as IMCF) in the rotational symmetric space with reasonable condition on its curvatures. In particular, we give a detailed analysis about the long time existence and the asymptotic behavior of the IMCF when the initial surface is closed star-shaped and mean-convex. We also present an application of the IMCF to the proof of the isoperimetric inequality for quermassintegrals of mean-convex star-shaped domains in Euclidean space. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-14T17:43:36Z (GMT). No. of bitstreams: 1 ntu-104-R01221014-1.pdf: 742544 bytes, checksum: 9a86b65c5a95adf35fe651df11d26ec6 (MD5) Previous issue date: 2015 | en |
| dc.description.tableofcontents | 致謝i
中文摘要ii Abstract iii 1. Introduction 1 2. Preliminary 5 3. The Geometry of Star-Shaped Hypersurfaces in a Rotationally Symmetric Space 10 4. The Inverse Mean Curvature Flow 19 5. Proof of Theorem 1.3 35 6. Proof of Theorem 1.4 39 References 41 | |
| dc.language.iso | en | |
| dc.subject | 逆平均曲率流 | zh_TW |
| dc.subject | Inverse Mean Curvature Flow | en |
| dc.title | 逆平均曲率流之研究 | zh_TW |
| dc.title | A Study of the Inverse Mean Curvature Flow | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 蔡忠潤(Chung-Jun Tsai),張樹城(Shun-Cheng Chang) | |
| dc.subject.keyword | 逆平均曲率流, | zh_TW |
| dc.subject.keyword | Inverse Mean Curvature Flow, | en |
| dc.relation.page | 41 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2015-12-03 | |
| 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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