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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/85451完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 蔡忠潤(Chung-Jun Tsai) | |
| dc.contributor.author | Chen-Kuan Lee | en |
| dc.contributor.author | 李宸寬 | zh_TW |
| dc.date.accessioned | 2023-03-19T23:16:47Z | - |
| dc.date.copyright | 2022-07-22 | |
| dc.date.issued | 2022 | |
| dc.date.submitted | 2022-07-18 | |
| dc.identifier.citation | [1] K. A. Brakke. The motion of a surface by its mean curvature, volume 20 of Mathematical Notes. Princeton University Press, Princeton, N.J., 1978. [2] W. Ding and Y. Yuan. Resolving the singularities of the minimal Hopf cones. J. Partial Differential Equations, 19(3):218–231, 2006. [3] D. Gilbarg and N. S. Trudinger. Elliptic partial differential equations of second order. Classics in Mathematics. Springer-Verlag, Berlin, 2001. Reprint of the 1998 edition. [4] R. S. Hamilton. Three-manifolds with positive Ricci curvature. J. Differential Geometry, 17(2):255–306, 1982. [5] R. Harvey and H. B. Lawson, Jr. Calibrated geometries. Acta Math., 148:47–157, 1982. [6] M. W. Hirsch, S. Smale, and R. L. Devaney. Differential equations, dynamical systems, and an introduction to chaos. Elsevier/Academic Press, Amsterdam, third edition, 2013. [7] G. Huisken. Flow by mean curvature of convex surfaces into spheres. J. Differential Geom., 20(1):237–266, 1984. [8] G. Huisken. Asymptotic behavior for singularities of the mean curvature flow. J. Differential Geom., 31(1):285–299, 1990. [9] G. R. Lawlor. A sufficient criterion for a cone to be area-minimizing. Mem. Amer. Math. Soc., 91(446):vi+111, 1991. [10] H. B. Lawson, Jr. and R. Osserman. Non-existence, non-uniqueness and irregularity of solutions to the minimal surface system. Acta Math., 139(1-2):1–17, 1977. [11] C. B. Morrey, Jr. Multiple integrals in the calculus of variations. Die Grundlehren der mathematischen Wissenschaften, Band 130. Springer-Verlag New York, Inc., New York, 1966. [12] X. Xu, L. Yang, and Y. Zhang. New area-minimizing Lawson-Osserman cones. Adv. Math., 330:739–762, 2018. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/85451 | - |
| dc.description.abstract | 在這篇論文中，我們首先得到基於羅森－歐斯曼錐構造的均曲流自相似解必須滿足的等式，並證明了自擴張解的存在性。主要的關鍵是利用羅森－歐斯曼錐的對稱性將偏微分方程轉化為常微分方程組，並研究這種近似於自治系統的常微分方程組。特別地，我們發現從狄利克雷問題的觀點來看，我們構造的自擴張解具唯一性。 | zh_TW |
| dc.description.abstract | In this thesis, we derived the equation of self-similar solutions to mean curvature flow based on the Lawson-Osserman cone and proved the existence of self-expander. The main point is to use the symmetry to transform the PDE into a system of ODEs and analyze such analogous autonomous system. In particular, the self-expander is unique form the viewpoint of Dirichlet problem. | en |
| dc.description.provenance | Made available in DSpace on 2023-03-19T23:16:47Z (GMT). No. of bitstreams: 1 U0001-0806202210173900.pdf: 1366535 bytes, checksum: f59655475c6aa05f85724d209b328236 (MD5) Previous issue date: 2022 | en |
| dc.description.tableofcontents | Contents Page Verification Letter from the Oral Examination Committee i Acknowledgements ii 摘要 iii Abstract iv Contents v 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Background materials . . . . . . . . . . . . . . . . . . . . . . . . 2 3 The desired ODE of self-similar solutions . . . . . . . . . . . . . . 4 4 An analogous autonomous system . . . . . . . . . . . . . . . . . . 6 5 The existence of self-expander . . . . . . . . . . . . . . . . . . . . 9 6 The uniqueness of self-expander from the perspective of Dirichlet problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 7 The behavior of the self-expander at infinity . . . . . . . . . . . . 15 References 18 Appendix — A brief view from power series expansion 19 | |
| dc.language.iso | en | |
| dc.subject | 幾何分析 | zh_TW |
| dc.subject | 狄利克雷問題 | zh_TW |
| dc.subject | 羅森－歐斯曼錐 | zh_TW |
| dc.subject | 自相似解 | zh_TW |
| dc.subject | 高餘維均曲流 | zh_TW |
| dc.subject | Self-Similar Solution | en |
| dc.subject | Mean Curvature Flow in Higher Codimensions | en |
| dc.subject | Geometric Analysis | en |
| dc.subject | Dirichlet Problem | en |
| dc.subject | Lawson-Osserman Cone | en |
| dc.title | 基於羅森－歐斯曼錐構造的均曲流自相似解 | zh_TW |
| dc.title | Self-similar solutions to the mean curvature flow based on the Lawson-Osserman cone | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 110-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.author-orcid | 0000-0002-4112-5921 | |
| dc.contributor.oralexamcommittee | 崔茂培(Mao-Pei Tsui),鄭日新(Jih-Hsin Cheng) | |
| dc.subject.keyword | 幾何分析,高餘維均曲流,自相似解,羅森－歐斯曼錐,狄利克雷問題, | zh_TW |
| dc.subject.keyword | Geometric Analysis,Mean Curvature Flow in Higher Codimensions,Self-Similar Solution,Lawson-Osserman Cone,Dirichlet Problem, | en |
| dc.relation.page | 22 | |
| dc.identifier.doi | 10.6342/NTU202200888 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2022-07-18 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| dc.date.embargo-lift | 2022-07-22 | - |
| 顯示於系所單位： | 數學系 | |
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