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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 梁惠禎(Fei-Tsen Liang) | |
| dc.contributor.author | Yi-Te Hong | en |
| dc.contributor.author | 洪亦德 | zh_TW |
| dc.date.accessioned | 2021-06-15T05:09:30Z | - |
| dc.date.available | 2010-07-28 | |
| dc.date.copyright | 2010-07-28 | |
| dc.date.issued | 2010 | |
| dc.date.submitted | 2010-07-23 | |
| dc.identifier.citation | Reference
[1]A. Aronszajn, A unique continuation theorem for solutions of elliptic partial di erential equations or inequalities of second order, J. Math. Pureappl. 1957, 236-249 [2]J. Lucas Barbosa and Manfredo do Carmo, A proof of a General Isoperimetric Inequality for surfaces, Math. Z. 162(1978), 245-261 [3]J. Lucas Barbosa and Manfredo do Carmo, Stability of Hypersurfaces with constant mean curvature, Math. Z. 185(1984), 339-353 [4]J. Lucas Barbosa, Manfredo do Carmo and Jost Eschenburg, Stability of Hypersurfaces of Constant Mean curvature in Riemannian Manifolds, Math. Z. 197(1988), 123-138 [5]Isaac Chavel and Edgar A. Feldman, Isoperimetric Inequalities on Curved Surfaces, Advances in Mathematics 37(1980), 83-98 [6]Isaac Chavel, Eigenvalues in Riemannian Geometry, Academic Press,1984 [7]Isaac Cheval, Riemannian Geometry. A Modern Introduction. Second Edition, Cambridge studies in advanced mathematics 98 (2006) [8]F. Fiala, Le problème des isopérimétres sur les surfaces ouvertes à courbure positive, Comment. Math. Helv. 13. (1941), 293-346 [9]M.E. Gage, Curve shortening makes convex curves circular, Invent. Math. 76(1984), 357-364 [10]M. Gage R. S. Hamilton, The Heat Equation shrinking convex plane curves, J. Diff. Geom. 23 (1986), 69-96 [11]Matthew A. Grayson, The Heat Equation shrinks Embedded plane curves to Round points, J. Di . Geom. 26 (1987) 285-314 [12]Matthew A. Grayson, Shortening embedded curves, Annals of Mathematics, 129 (1989), 71-111 [13]Joel Hass and Frank Morgan, Geodesics and soap bubbles in surfaces, Math. Z. 223 (1996), 185- 196 [14]H. Howards, M. Hutchings and F. Morgan, The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature, Trans. Amer. Math. Soc., 352(11) (2000), 4889-4909 [15]R. Narasimhan, Analysis on Real and Complex Manifolds, North-Holland Mathematical Library vol. 35 [16]Robert Osserman, The isoperimetric inequality. Bulletin of the American Mathematical society v.84, no.6 1978, 1182-1238 [17]Robert Osserman, Bonnesen-style isoperimetric inequalities, Amer. Math. Monthly, 86(1) (1979), 1-29 [18]Manuel Ritoré, Constant geodesic curvature curves and isoperimetric domains in rotationally symmetric surfaces, Comm. Anal. Geom. 9 (2001), 1093-1138. [19]Peter Topping, Mean curvature flow and geometric inequalities, J. Reine angew. Math. 503 (1998), 47-61 [20]Peter Topping, The isoperimetric inequality on a surface, manuscripta math, 100 (1999), 23-33 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/46447 | - |
| dc.description.abstract | 文中討論球面上（旋轉對稱同時對赤道對稱在北半球與南半球
分別有單調高斯曲率）的等周長問題的解，使用Sturm’s 比較 定理來分析得出以最短周長包圍面積的區域形狀。 | zh_TW |
| dc.description.abstract | In the thesis we follow the demonstration of Prof. M. Ritoré to solve the isoperimetric problem on roatationally and equatorially symmetric spheres with monotone Gauss curvature from the poles. We first classify all the curves with constant geodesic curvature on a sphere with the above properties. Then we apply Sturm's comparison theorem successively to get the final only possible curve enclosing an isoperimetric domain. On regions with constant Gauss curvature we also invoke the Bol-Fiala inequality to conclude that inside such regions a geodesic circle has the
minimal length encircling a domain with a given area. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T05:09:30Z (GMT). No. of bitstreams: 1 ntu-99-R96221018-1.pdf: 500582 bytes, checksum: ceb3d4a3da363eefc71d1862b3a77f17 (MD5) Previous issue date: 2010 | en |
| dc.description.tableofcontents | 目 錄
口試委員會審定書........................................i 誌謝...................................................ii 中文摘要..............................................iii 英文摘要...............................................iv 第一章 Introduction.....................................1 第二章 Existence....................................... 3 第三章 First and Second Variations of Area and the notion of Stability............................................6 3.1 First Variation of Area.............................6 3.2 Second variational formula for J and its relation with the second variation of area for a volume-preserving variation that fixes boundary...........................9 第四章 Isoperimetric Problem on rotationally and equatorial symmetric spheres with mototone Gauss curvature from the equator................................................15 第五章 Bol-Fiala inequality............................31 5.1 A derivation of Bol-Fiala inequality...............31 5.2 A generalization using curve shortening theorem....40 第六章 Appendix........................................43 參考文獻...............................................49 | |
| dc.language.iso | en | |
| dc.title | 關於二維旋轉對稱球面之等周長問題的討論 | zh_TW |
| dc.title | A discussion of the isoperimetric problem on spheres with
rotational and equatorial symmetry and monotone Gauss curvature | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 98-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 謝春忠(Chun-Chung Hsieh),王藹農(Ai-Nung Wang) | |
| dc.subject.keyword | 二維球面等周長問題,穩定性, | zh_TW |
| dc.subject.keyword | Isoperimetric problem on spheres,Bol-Fiala inequality,stability, | en |
| dc.relation.page | 50 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2010-07-26 | |
| 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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