請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8267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 | Han-Chung Wu | en |
| dc.contributor.author | 吳漢中 | zh_TW |
| dc.date.accessioned | 2021-05-20T00:51:00Z | - |
| dc.date.available | 2020-08-20 | |
| dc.date.available | 2021-05-20T00:51:00Z | - |
| dc.date.copyright | 2020-08-20 | |
| dc.date.issued | 2020 | |
| dc.date.submitted | 2020-08-14 | |
| dc.identifier.citation | A. Bobenko and U. Pinkall, “Discrete isothermic surfaces,” J. Reine Angew. Math., vol. 475, pp. 187–208, 1996. [Online]. Available: https://doi.org/10.1515/crll.1996.475.187 U. Dierkes, S. Hildebrandt, and F. Sauvigny, Minimal surfaces, 2nd ed., ser. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer, Heidelberg, 2010, vol. 339, with assistance and contributions by A. Küster and R. Jakob. [Online]. Available: https://doi.org/10.1007/978-3-642-11698-8 M. Kotani, H. Naito, and T. Omori, “A discrete surface theory,” Comput. Aided Geom. Design, vol. 58, pp. 24–54, 2017. [Online]. Available: https://doi.org/10.1016/j.cagd.2017.09.002 U. Pinkall and K. Polthier, “Computing discrete minimal surfaces and their conjugates,” Experiment. Math., vol. 2, no. 1, pp. 15–36, 1993. [Online]. Available: http://projecteuclid.org/euclid.em/1062620735 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8267 | - |
| dc.description.abstract | 在本篇論文，我們主要是探討M. Kotani, H. Naito and T. Omori ([3]) 所提出的離散曲面理論。我們首先回顧他們論文的總體結果。然後我們討論了斜線四面體的平均曲率流的行為以及離散曲率和高斯-博內定理的收斂問題。 | zh_TW |
| dc.description.abstract | In this thesis, we discuss discrete surface theories developed by M. Kotani, H. Naito and T. Omori in ([3]). We first review the general results from their paper. Then we discuss the behavior of the mean curvature flow of skew line tetrahedron and the issue of the convergence of discrete curvatures and Gauss-Bonnet Theorem. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-20T00:51:00Z (GMT). No. of bitstreams: 1 U0001-1108202006455700.pdf: 2450695 bytes, checksum: a906222644fd2c57c86b08e0679b93c6 (MD5) Previous issue date: 2020 | en |
| dc.description.tableofcontents | 口試委員會審定書 i 誌謝 ii 摘要 iii Abstract iv Table of Contents v List of Figures vi 1 The classical surface theory in R^3 1 2 A surface theory for graphs in R^3 6 2.1 Definition of curvatures 6 2.2 Harmonic and minimal surface 15 3 Discrere surface structure on a sphere 19 3.1 Plane graphs 19 3.2 Sphere-shaped graphs 19 4 Mean curvature flow 31 4.1 M.C.F. of regular tetrahedron 31 4.2 M.C.F. of perpendicular skew line tetrahedron 34 5 Convergence of discrete curvatures 41 5.1 Convergence theorem 41 5.2 Convergence of sphere 43 6 Gauss-Bonnet Theorem 50 6.1 Discrete Gauss-Bonnet Theorem 50 6.2 Numerical computations for convergence of Gauss-Bonnet Theorem on sphere 51 References 53 | |
| dc.language.iso | en | |
| dc.title | 離散曲面理論之探討 | zh_TW |
| dc.title | A survey on discrete surface theory | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 108-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 蔡忠潤(Chung-Jun Tsai),陳宜良(I-Liang Chern) | |
| dc.subject.keyword | 離散曲面,平均曲率,高斯曲率, | zh_TW |
| dc.subject.keyword | discrete surface,mean curvature,Gauss curvature, | en |
| dc.relation.page | 53 | |
| dc.identifier.doi | 10.6342/NTU202002893 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2020-08-14 | |
| 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 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| U0001-1108202006455700.pdf | 2.39 MB | Adobe PDF | 檢視/開啟 |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。