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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 | Yen-Wen Fan | en |
dc.contributor.author | 樊彥彣 | zh_TW |
dc.date.accessioned | 2021-05-15T17:56:14Z | - |
dc.date.available | 2014-07-29 | |
dc.date.available | 2021-05-15T17:56:14Z | - |
dc.date.copyright | 2014-07-29 | |
dc.date.issued | 2014 | |
dc.date.submitted | 2014-07-02 | |
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dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/5336 | - |
dc.description.abstract | 這篇文章包含三大部分,第一部分證明矩陣形式的 Li-Yau-Hamilton Harnack 不等式。第二部份延續第一部分的工作,推廣至(1,1)-form 形式的 Li-Yau-Hamilton Harnack 不等式。第三部份將應用這不等式証明柯西黎曼上的 Gap 定理。 | zh_TW |
dc.description.abstract | In the first part of thesis, we first derive the CR analogue of matrix Li-Yau-Hamilton
inequality for a positive solution to the CR heat equation in a closed pseudohermitian (2n+1)- manifold with nonnegative bisectional curvature and bitorsional tensor. We then obtain the CR Li-Yau gradient estimate in a standard Heisenberg group. Finally, we extend the CR matrix Li-Yau-Hamilton inequality to the case of Heisenberg groups. As a consequence, we derive the Hessian comparison property in the standard Heisenberg group. In the second part, we study the CR Lichnerowicz-Laplacian heat equation deformation of (1; 1)-tensors on a complete strictly pseudoconvex CR (2n+1)-manifold and derive the linear trace version of Li-Yau-Hamilton inequality for positive solutions of the CR Lichnerowicz- Laplacian heat equation. We also obtain a nonlinear version of Li-Yau-Hamilton inequality for the CR Lichnerowicz-Laplacian heat equation coupled with the CR Yamabe flow and trace Harnack inequality for the CR Yamabe flow. In the last part, by applying a linear trace Li-Yau-Hamilton inequality for a positive (1; 1)-form solution of the CR Hodge-Laplace heat equation and monotonicity of the heat equation deformation, we obtain an optimal gap theorem for a complete strictly pseudocovex CR (2n+1)-manifold with nonnegative pseudohermitian bisectional curvature and vanishing torsion. We prove that if the average of the Tanaka-Webster scalar curvature over a ball of radius r centered at some point o decays as o(r^-2 ), then the manifold is flat. | en |
dc.description.provenance | Made available in DSpace on 2021-05-15T17:56:14Z (GMT). No. of bitstreams: 1 ntu-103-D98221003-1.pdf: 756411 bytes, checksum: 4c4557c1e09e161a9da68ff07a932c2f (MD5) Previous issue date: 2014 | en |
dc.description.tableofcontents | 1. Abstract v
2. Introduction 1 2.1. CR Li-Yau Gradient Estimate and Harnack Inequality 2 2.2. CR Matrix Li-Yau-Hamilton Inequality 4 2.3. CR Linear Trace Li-Yau-Hamilton Inequality and Gap Theorem 6 2.4. The Coupled CR Yamabe Flow 7 3. Preliminary 10 4. CR Matrix Li-Yau-Hamilton Harnack Inequality 12 4.1. CR Matrix Li-Yau-Hamilton Inequality 15 4.2. The CR Gradient Estimate and Harnack inequality in Heisenberg Groups 20 4.3. Complete noncompact case 25 5. Linear Trace Li-Yau-Hamilton inequality 31 5.1. The CR Bochner-Weitzenbock Formula 35 5.2. Linear Trace Li-Yau-Hamilton Inequality 39 5.3. Nonlinear Version for Li-Yau-Hamilton Inequality 50 6. CR Gap Theorem 58 6.1. CR Moment-Type Estimates 59 6.2. CR Lichnerowicz-Laplacian heat equation 63 6.3. Proof of CR Optimal Gap Theorem 67 Appendix A. 71 References 74 | |
dc.language.iso | en | |
dc.title | 柯西黎曼 Li-Yau-Hamilton 不等式即其應用 | zh_TW |
dc.title | CR Li-Yau-Hamilton Inequality and its Applications | en |
dc.type | Thesis | |
dc.date.schoolyear | 102-2 | |
dc.description.degree | 博士 | |
dc.contributor.oralexamcommittee | 張德健(Der-Cheng Chang),林俊吉(Chun-Chi Lin),褚孫錦(Sun-Chin Chu),徐淑裕(Shu-Yu Hsu),吳進通(Chin-Tung Wu) | |
dc.subject.keyword | 擬埃爾米特,Li-Yau-Hamilton,Gap 定理,Harnack 不等式, | zh_TW |
dc.subject.keyword | Li-Yau-Hamilton,Gap theorem,CR manifold,Harnack, | en |
dc.relation.page | 77 | |
dc.rights.note | 同意授權(全球公開) | |
dc.date.accepted | 2014-07-02 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 數學研究所 | zh_TW |
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