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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/67815完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 張樹城(Shu-Cheng Chang) | |
| dc.contributor.author | Keng-Hung Steven Lin | en |
| dc.contributor.author | 林耿弘 | zh_TW |
| dc.date.accessioned | 2021-06-17T01:51:32Z | - |
| dc.date.available | 2018-07-28 | |
| dc.date.copyright | 2017-07-28 | |
| dc.date.issued | 2017 | |
| dc.date.submitted | 2017-07-24 | |
| dc.identifier.citation | [1] A. Greenleaf, The First Eigenvalue of a Sublaplacian on a Pseudohermitian Manifold, Comm. Part. Diff. Equ. 10(2) (1985), no.3 191–217.
[2] C. R. Graham and J. M. Lee, Smooth Solutions of Degenerate Laplacians on Strictly Pseudoconvex Domains, Duke Math. J., 57 (1988), 697-720. [3] H. I. Choi and A. N. Wang, A First Eigenvalue Estimate for Minimal Hypersurfaces, J. Diff. Geom. 18 (1983), 559-562. [4] J. M. Lee, Pseudo-Einstein Structure on CR Manifolds, Amer. J. Math. 110 (1988), 157-178. [5] J. M. Lee, The Fefferman Metric and Pseudohermitian Invariants, Trans. A.M.S. 296 (1986), 411-429. [6] R. Reilly, Applications of the Hessian Operator in a Riemannian Manifold, Indiana U.Math. J. 26 (1977), 459-472. [7] Shu-Cheng Chang, Chih-Wei Chen, Chin-Tung Wu, On the CR Analogue of Reilly Formula and Yau Eigenvalue Conjecture, arXiv:1503.07639v2, (2015). [8] Shu-Cheng Chang, Hung-Lin Chiu, On the CR Analogue of Obataȷs Theorem in a Pseudohermitian 3-Manifold, Math. Ann. Vol. 345, No. 1 (2009), 33-51. [9] Shu-Cheng Chang, Hung-Lin Chiu, On the Estimate of the First Eigenvalue of a Sublaplacian on a Pseudohermitian 3-Manifold, Pacific J. Math., Vol232(2007), 269-282. [10] Shu-Cheng Chang, Jin-Hsin Cheng, Hung-Lin Chiu, The Fourth Order Curvature Flow on a CR 3-Manifold, Indiana Univ. Math.J., Vol. 56, No. 4 (2007), 1793-1826. [11] Sorin Dragomir, Giuseppe Tomassini, Differential Geometry and Analysis on CR Manifolds, ISBN: 978-0-8176-4388-1, Birkhäuser Boston, (2006). [12] P. Li, Geometric Analysis, ISBN: 9781107020641, Cambridge University Press, (2012). | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/67815 | - |
| dc.description.abstract | 在本文中，作者在一個搭配特殊條件下有權重的三維的封閉擬埃爾米特流形上，給出加權柯西-黎曼萊利形式方程，並在同樣條件下利用該方程給出該流形上的韋頓-子拉普拉斯算子(Witten sub-Laplacian)的一個第一特徵值的一個下界。 | zh_TW |
| dc.description.abstract | In this thesis, I derive a weighted CR-Reilly’s type equation on a 3-dimensional closed weighted pseudohermitian manifold under some assumptions, and obtain a lower bound estimate for the first eigenvalue of the Witten sub-Laplacian operator on a 3-dimensional closed weighted pseudohermitian manifold under the same assumptions. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T01:51:32Z (GMT). No. of bitstreams: 1 ntu-106-R02221008-1.pdf: 490246 bytes, checksum: 4afd968dc4907916384fb3a3e57a717d (MD5) Previous issue date: 2017 | en |
| dc.description.tableofcontents | 誌謝 ii
中文摘要 iv Abstract v Contents vi 1 Introduction 1 2 Weighted CR-Reilly’s Type Equation 7 3 A Lower Bound Estimate of the Fourth-Ordered Differetial Operator 15 4 A First Eignevalue Esitmate of Lϕ 25 A A Brief Introduction to Psuedohermitian Geometry 29 B Bibliography 35 | |
| dc.language.iso | en | |
| dc.subject | 柯西-黎曼幾何 | zh_TW |
| dc.subject | 幾何分析 | zh_TW |
| dc.subject | 加權擬埃爾米特流形 | zh_TW |
| dc.subject | 韋頓-子 拉普拉斯算子 | zh_TW |
| dc.subject | 四階微分算子 | zh_TW |
| dc.subject | 第一特徵值下界估計 | zh_TW |
| dc.subject | first eigenvalue estimate | en |
| dc.subject | CR geometry | en |
| dc.subject | Witten sub-Laplacian operator | en |
| dc.subject | four-ordered differential operator | en |
| dc.subject | geometric analysis | en |
| dc.subject | weighted pseudohermitian manifold | en |
| dc.title | 三維封閉加權擬埃爾米特流形上韋頓-子拉普拉斯算子第一特徵值之下界估計 | zh_TW |
| dc.title | A First Eigenvalue Estimate of Witten sub-Laplacian Operator on
Three-Dimensional Closed Weighted Pseudo-Hermitian Manifold | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 105-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳瑞堂(Jui-Tang Chen),吳進通(Chin-Tung Wu) | |
| dc.subject.keyword | 柯西-黎曼幾何,幾何分析,加權擬埃爾米特流形,韋頓-子 拉普拉斯算子,四階微分算子,第一特徵值下界估計, | zh_TW |
| dc.subject.keyword | CR geometry,geometric analysis,weighted pseudohermitian manifold,Witten sub-Laplacian operator,four-ordered differential operator,first eigenvalue estimate, | en |
| dc.relation.page | 37 | |
| dc.identifier.doi | 10.6342/NTU201701755 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2017-07-25 | |
| 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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