請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/58705完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 蕭欽玉(Chin-Yu Hsiao) | |
| dc.contributor.author | Ching-Hsien Lee | en |
| dc.contributor.author | 李京憲 | zh_TW |
| dc.date.accessioned | 2021-06-16T08:26:38Z | - |
| dc.date.available | 2020-07-17 | |
| dc.date.copyright | 2020-07-17 | |
| dc.date.issued | 2020 | |
| dc.date.submitted | 2020-07-13 | |
| dc.identifier.citation | [1] John W. Milnor. Morse theory. Princeton University Press, 1963. ISBN: 978-0691080086. [2] Liviu Nicolaescu. An invitatioin to Morse Theory. New York: Springer, 2011. ISBN: 978-1-4614-1104-8. [3] Michael Reed and Barry Simon. Methods of modern mathematical physics. II. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1975. ISBN: 0-12-585002-6(v.2). [4] Frank Warner. Foundations of differentiable manifolds and Lie groups. New York: Springer, 1983. ISBN: 978-0387908946. [5] Edward Witten. Supersymmetry and morse theory. J. DIfferential Geometry, 17(4):661–692, 1982. doi: 10.4310/jdg/1214437492. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/58705 | - |
| dc.description.abstract | 在這篇碩士論文中，我們用維騰形變的方法去計算維騰算子的密度函數並且整理維騰證明摩斯定理的方法。透過密度函數的漸進行為 我們可以更進一步導出維騰拉普拉斯算子特徵空間的維度。密度函數的漸進行為在探討非緊緻流形扮演了一個重要的角色。 | zh_TW |
| dc.description.abstract | In this article, we calculate local density function for Witten Laplacian by using the techniques of Witten's deformation and his proof of Morse inequality. With the help of local density function, we can further derive dimension of the eigenspaces of Witten Laplace operator. The asymptotic behaviour for local density function plays an important role in non-compact case. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T08:26:38Z (GMT). No. of bitstreams: 1 U0001-1007202018204200.pdf: 3663470 bytes, checksum: ba5f3e0b023bfd180d8d023619c44b1c (MD5) Previous issue date: 2020 | en |
| dc.description.tableofcontents | Abstract i 1 Introduction 1 2 Preliminaries 7 2.1 Some Basics of Differential Geometry . . . . . . . . . . . . . . 7 2.2 Laplace-Beltrami operator On Manifolds . . . . . . . . . . . . 10 2.3 Norms on Ω(M) . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3.1 Metric of Tensors . . . . . . . . . . . . . . . . . . . . . 12 2.3.2 Ck-norm of smooth functions . . . . . . . . . . . . . . 12 2.3.3 Sobolev space and norm on Ω(M) . . . . . . . . . . . . 13 3 Witten Deformation of Laplace Operator 14 3.1 Deformed de Rham Cohomology . . . . . . . . . . . . . . . . 14 3.2 Witten Laplace Operator . . . . . . . . . . . . . . . . . . . . . 15 3.3 Eigenspace of Witten Laplace Operator . . . . . . . . . . . . . 18 3.4 Locally Flat Metric Near Critical Points . . . . . . . . . . . . 21 3.5 Witten Laplace Operator with Flat Metric . . . . . . . . . . . 22 4 A Study on Eigenspaces 24 Reference 46 | |
| dc.language.iso | en | |
| dc.subject | 量子諧振子 | zh_TW |
| dc.subject | 緊緻流形 | zh_TW |
| dc.subject | 維騰拉普拉斯算子 | zh_TW |
| dc.subject | 摩斯定理 | zh_TW |
| dc.subject | compact manifold | en |
| dc.subject | quantum harmonic oscillator | en |
| dc.subject | Morse theory | en |
| dc.subject | Witten Laplacian | en |
| dc.title | 維騰拉普拉斯算子的密度函數在緊緻流形的漸進行為 | zh_TW |
| dc.title | Asymptotic Behaviour of The Density Function of Witten Laplacian on Compact Manifolds | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 108-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 黃榮宗(Rung-Tzung Huang),鄭日新(Jih-Hsin Cheng),蔡宜洵(I-Hsun Tsai) | |
| dc.subject.keyword | 緊緻流形,量子諧振子,摩斯定理,維騰拉普拉斯算子, | zh_TW |
| dc.subject.keyword | compact manifold,quantum harmonic oscillator,Morse theory,Witten Laplacian, | en |
| dc.relation.page | 46 | |
| dc.identifier.doi | 10.6342/NTU202001434 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2020-07-13 | |
| 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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