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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/796完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 王藹農(Ai-Nung Wang) | |
| dc.contributor.author | Wei-Hung Liao | en |
| dc.contributor.author | 廖偉宏 | zh_TW |
| dc.date.accessioned | 2021-05-11T05:05:44Z | - |
| dc.date.available | 2020-07-02 | |
| dc.date.available | 2021-05-11T05:05:44Z | - |
| dc.date.copyright | 2019-07-02 | |
| dc.date.issued | 2019 | |
| dc.date.submitted | 2019-06-05 | |
| dc.identifier.citation | [1] Almgren, F.J., 1976. Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints. American Mathematical Soc., 165.
[2] Anderson, M.T., 1982. Complete minimal varieties in hyperbolic space. Inventiones mathematicae, 69(3), pp.477-494. [3] Brakke, K.A., 2015. The Motion of a Surface by Its Mean Curvature. Princeton Uni-versity Press, (MN-20). [4] Colding, T.H. and Minicozzi, W.P., 2012. Generic mean curvature flow I: generic sin-gularities. Annals of mathematics, pp.755-833. [5] Fleming, W.H., 1966. Flat chains over a finite coefficient group. Transactions of the American mathematical society, 121(1), pp.160-186. [6] Freire, A., 2010. Mean curvature motion of triple junctions of graphs in two dimensions. Communications in Partial Differential Equations, 35(2), pp.302-327. [7] Huisken, G., 1990. Asymptotic-behavior for singularities of the mean-curvature flow. Journal of Differential Geometry, 31(1), pp.285-299. [8] Ilmanen, T., 1994. Elliptic regularization and partial regularity for motion by mean curvature. American Mathematical Soc., 520. [9] Ilmanen, T., Neves, A. and Schulze, F., 2019. On short time existence for the planar network flow. J. Differential Geom. 111(1), pp.39-89. [10] Jensen, G.R., Musso, E. and Nicolodi, L., 2016. Surfaces in classical geometries: a treatment by moving frames. Springer. [11] Jorge, L.P. and Meeks III, W.H., 1983. The topology of complete minimal surfaces of finite total Gaussian curvature. Topology, 22(2), pp.203-221. [12] Kim, L. and Tonegawa., 2017. On the mean curvature flow of grain boundaries. Annales de l’Institut Fourier, 67(1), pp. 43-142. [13] Lawlor, G. and Morgan, F., 1994. Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms. Pacific journal of Mathematics, 166(1), pp.55-83. [14] W.H.,Mantegazza, C., Novaga, M. and Pluda, A., 2016. Motion by curvature of networks with two triple junctions. Geometric Flows, 2(1), pp.18-48. [15] Mantegazza, C., Novaga, M. and Tortorelli, V.M., 2004. Motion by curvature of planar networks. Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 3(2), pp.235-324. [16] Mazzeo, R. and Saez, M., 2007. Self-similar expanding solutions for the planar network flow. Analytic aspects of problems in Riemannian geometry: Elliptic PDEs, solitons and computer imaging, 22, pp.159-173 [17] Morgan, F., 1989. Size-minimizing rectifiable currents. Inventiones mathematicae, 96(2), pp.333-348. [18] Morgan, F., 2016. Geometric measure theory: a beginner’s guide. Academic press. [19] Mullins, W.W., 1956. Two-dimensional motion of idealized grain boundaries. Journal of Applied Physics, 27(8), pp.900-904. [20] Plateau, J., 1873. Statique exp´erimentale et th´eorique des liquides soumis aux seules forces mol´eculaires. Gauthier-Villars, 2 [21] Schoen, R.M., 1983. Uniqueness, symmetry, and embeddedness of minimal surfaces. Journal of Differential Geometry, 18(4), pp.791-809. [22] Schulze, F. and White, B., 2018. A local regularity theorem for mean curvature flow with triple edges. Journal f¨ur die reine und angewandte Mathematik (Crelles Journal). [23] Taylor, J.E., 1976. The structure of singularities in solutions to ellipsoidal variational problems with constraints in R3. Annals of Mathematics, pp.541-546. [24] White, B., 1996. Existence of least-energy configurations of immiscible fluids. Journal of Geometric Analysis, 6(1), pp.151-161. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/handle/123456789/796 | - |
| dc.description.abstract | 我們考慮由有限多個通過原點的曲面所組成的多相曲面C0,其中所有的一維結線是由三曲面兩兩夾角相同所組合形成的。此外各曲面對原點做徑向投影所形成的曲線也是有限長。我們證明了以此C0做初始條件下存在一多相均曲率流的自相似擴張解,而這組解是由那些正規三結線和正規四節點所組合出來的曲面。 | zh_TW |
| dc.description.abstract | We consider a multiphase surface C0 in R3 consisting of a finite number of surfaces passing through the origin , where all 1-dimensional junctions are regular triple junctions in which three planes meet at the same angle and each surface scales down homothetically to a limit curve of finite length. We prove the existence of self-similar expanding solutions of the mean curvature flow on the multiphase surface initially given by C0. For this initial C0, there are multiple solutions that are combinations of the regular triple junctions and regular quadruple points, where four regular triple junctions meet at an angle of approximately 109.5◦. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-11T05:05:44Z (GMT). No. of bitstreams: 1 ntu-108-D01221002-1.pdf: 4299359 bytes, checksum: ac264e21cc9d863a4aaff01d9e833825 (MD5) Previous issue date: 2019 | en |
| dc.description.tableofcontents | 1.Introduction 1
2.Multiphase Surfaces 3 2.1 Definition..................................................3 2.2 Examples....................................................4 2.3 Existence...................................................5 3.Relation between Poincare ball model and Euclidean space 8 4.Self-expanding Solutions to the Multiphase Mean Curvature Flow 10 4.1 Smooth Case.................................................10 4.2 Singular Case...............................................11 4.3 Asymptotic Behaviors........................................13 5.Proof of Main Theorem 16 5.1 Flat 2-dimensional Chains F2(R3, Zk+1)......................16 5.1.1 Introduction...........................................16 5.1.2 Example................................................17 5.2 Existence in a Bounded Domain...............................18 5.3 Existence in an Unbounded Domain............................20 6.Appendix 22 6.1 Equivalent Condition of the Skewness Property...............22 6.2 First variation around the Singular Structures..............24 Bibliography 33 | |
| dc.language.iso | en | |
| dc.subject | 自相似擴張解 | zh_TW |
| dc.subject | 多相均曲率流 | zh_TW |
| dc.subject | Self-similar | en |
| dc.subject | Mean Curvature Flow | en |
| dc.subject | Multiphase | en |
| dc.title | 多相均曲率流的自相似擴張解 | zh_TW |
| dc.title | Self-similar Expanding Solutions for a Multiphase Mean Curvature Flow | en |
| dc.date.schoolyear | 107-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 張樹城(Shun-Cheng Chang),陳其誠(Ki-Seng Tan),崔茂培(Mao-Pei Tsui),翁秉仁(Ping-Zen Ong),梁惠禎(Fei-Tsen Liang) | |
| dc.subject.keyword | 多相均曲率流,自相似擴張解, | zh_TW |
| dc.subject.keyword | Multiphase,Self-similar,Mean Curvature Flow, | en |
| dc.relation.page | 35 | |
| dc.identifier.doi | 10.6342/NTU201900823 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2019-06-06 | |
| 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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