1997/08/12 by Boris Shapiro, Shapiro, Boris
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #dg-ga #math.DG
paper · pdf · doi:10.48550/arxiv.dg-ga/9708009
AMSTeX-file with 10 pictures enclosed as eps-files, 18 pages, to appear in the AMS-volume on knots and curves, editor S.Tabachnikov, also available at the homepage http://www.matematik.su.se/~shapiro/
arxiv created 1997/08/12 · openalex publication_date 1997/08/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a criterion when a planar tree-like curve, i.e. a generic immersed plane curve each double point of which cuts it into two disjoint parts, can be send by a diffeomorphism of the plane onto a curve with no inflection points. We also present some upper and lower bounds for the minimal number of inflection points on such curves unremovable by diffeomorphisms of the plane in terms of their combinatorics.