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研究生： 洪旻楷
Hung, Min-Kai
論文名稱： On the finiteness of geometric knots
On the finiteness of geometric knots
指導教授： 林俊吉
Lin, Chun-Chi
學位類別： 碩士
Master
系所名稱： 數學系
Department of Mathematics
論文出版年： 2010
畢業學年度： 98
語文別： 英文
論文頁數： 27
中文關鍵詞： 結 、正交投影能 、平均交叉數 、厚度 、總曲率 、結型
英文關鍵詞： knots, normal projection energy, average crossing number, thickness, total curvature, knot type
DOI URL： https://doi.org/10.6345/NTNU202201817
論文種類： 學術論文
相關次數： 點閱：126  下載：1 
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    • 在這篇文章中，我們考慮Normal Projection Energy的一些性質。首先，在$C^{1,1}$平滑性下的Knot，有上界之Normal Projection Energy給出Knot的Gromov's distortion下界。接著，Normal Projection Energy可由total curvature和ropelength之乘積涵蓋住。最後，為求Normal Projection Energy的涵蓋界，我們考慮一類包含在球中並給定端點和總長之曲線的total curvature。

    In these paper, we consider several properties of Normal Projection Energy. Firstly, among the class of $C^{1,1}$-smooth knots, the upper bound of Normal Projection Energy gives a uniform lower bound of Gromov's distorsion of knots. Secondly, Normal Projection Energy is bounded by the product of total curvature and ropelength. Thirdly, to prove the bound of Normal Projection Energy, we study the curves which attain the infimum of the total absolute curvature in the set of curves contained in a ball with fixed endpoints and length.

    1. Introduction........................................1 2. Lower bounds for thickness of knots or links as a function of their Normal Projection Energy.............3 3. The total absolute curvature of piecewise $C^{2}$ open curve in $R^{3}$......................................14 4. A upper bound of Normal Projection Energy and Finiteness of Knot Type...............................18 5. References.........................................26

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