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研究生: 崔庭緯
Tsui, Ting-Wei
論文名稱: On the least number of orthogonal geodesic chords of convex domain
On the least number of orthogonal geodesic chords of convex domain
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: 2019
畢業學年度: 107
語文別: 英文
論文頁數: 11
中文關鍵詞: Orthogonal geodesic chordWidth function
英文關鍵詞: Orthogonal geodesic chord, Width function
DOI URL: http://doi.org/10.6345/NTNU201900270
論文種類: 學術論文
相關次數: 點閱:130下載:11
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  • 無中文摘要

    In this article we try to combine the concepts: Orthogonal geodesic chord and Width function and give a sufficient condition to preserve the least number of orthogonal geodesic chords of a convex plane curve.

    1 Introduction 2 2 Definitions and theories 4 2.1 Width function 4 2.2 Width function and O.G.C 6 2.3 Main theorem 7 3 Preparation for higher dimension 9 Bibliography 11

    [1] Herbert Busemann. The Geometry of Geodesics, page 155. Dover Publications, 2005.

    [2] V. G. Boltyanski I. M. Yaglom. Convex figures, page 8. Holt, Rinehart
    and Winston, 1961.

    [3] Nicolaas H. Kuiper. Double normals of convex bodies. Israel Journal of
    Mathematics, 2:71–80, 1964.

    [4] L. Schnirelmann L. Lusternik. Methodes topologiques dans les problemes
    variationnels. Hermann, 1934.

    [5] Martin Li. Chord shortening flow and a theorem of lusternik and
    schnirelmann. Pacific J. Math, 299:469–488, 2017.

    [6] Serge Tabachnikov. The four-vertex theorem revisited–two variations on
    the old theme. American Mathematical Monthly, 102:912–916.

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