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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Carathéodory conjecture ： ウィキペディア英語版 Carathéodory conjecture In differential geometry, the Carathéodory conjecture is a mathematical conjecture attributed to Constantin Carathéodory by Hans Ludwig Hamburger in a session of the Berlin Mathematical Society in 1924.〔''Sitzungsberichte der Berliner Mathematischen Gesellschaft'', 210. Sitzung am 26. März 1924, Dieterichsche Universitätsbuchdruckerei, Göttingen 1924〕 Carathéodory did publish a paper on a related subject,〔''Einfache Bemerkungen über Nabelpunktskurven'', in: Festschrift 25 Jahre Technische Hochschule Breslau zur Feier ihres 25jährigen Bestehens, 1910—1935, Verlag W. G. Korn, Breslau, 1935, pp 105 - 107, and in: Constantin Carathéodory, Gesammelte Mathematische Schriften, Verlag C. H. Beck, München, 1957, vol 5, 26–30〕 but never committed the Conjecture into writing. In,〔''A mathematician's miscellany'', Nabu Press (August 31, 2011) ISBN 978-1179121512〕 John Edensor Littlewood mentions the Conjecture and Hamburger's contribution 〔H. Hamburger, ''Beweis einer Caratheodoryschen Vermutung. I'', Ann. Math. (2) 41, 63—86 (1940); ''Beweis einer Caratheodoryschen Vermutung. II'', Acta Math. 73, 175—228 (1941), and ''Beweis einer Caratheodoryschen Vermutung. III'', Acta Math. 73, 229—332 (1941)〕 as an example of a mathematical claim that is easy to state but difficult to prove. Dirk Struik describes in 〔D. J. Struik, (''Differential Geometry in the large'' ), Bull. Amer. Math. Soc. 37, No 2, 49—62 (1931). 〕 the formal analogy of the Conjecture with the Four Vertex Theorem for plane curves. Modern references to the Conjecture are the problem list of Shing-Tung Yau,〔S. T. Yau, ''Problem Section p. 684'', in: Seminar on Differential Geometry, ed. S.T. Yau, Annals of Mathematics Studies 102, Princeton 1982〕 the books of Marcel Berger,〔M. Berger, ''A Panoramic View of Riemannian Geometry'', Springer 2003 ISBN 3-540-65317-1〕〔M. Berger,''Geometry Revealed: A Jacob's Ladder to Modern Higher Geometry'' , Springer 2010 ISBN 3-540-70996-7〕 as well as the books.〔I. Nikolaev, ''Foliations on Surfaces'' , Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A, Series of Modern Surveys in Mathematics, Springer 2001 ISBN 3-540-67524-8〕〔D. J. Struik, ''Lectures on Classical Differential Geometry'', Dover 1978 ISBN 0-486-65609-8〕〔V. A. Toponogov, ''Differential Geometry of Curves and Surfaces: A Concise Guide'', Birkhäuser, Boston 2006 ISBN 978-0-8176-4402-4〕〔R.V. Gamkrelidze (Ed.), ''Geometry I: Basic Ideas and Concepts of Differential Geometry '', Encyclopaedia of Mathematical Sciences, Springer 1991 ISBN 0-387-51999-8〕 ==Mathematical content== The Conjecture claims that any convex, closed and sufficiently smooth surface in three dimensional Euclidean space needs to admit at least two umbilic points. In the sense of the Conjecture, the spheroid with only two umbilic points and the sphere, all points of which are umbilic, are examples of surfaces with minimal and maximal numbers of umbilics. For the conjecture to be well posed, or the umbilic points to be well-defined, the surface needs to be at least twice differentiable. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Carathéodory conjecture」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.