2005/11/21 by Gianmarco Capitanio, Capitanio, Gianmarco
Mathematics · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Analytic and geometric function theory
paper · doi:10.48550/arxiv.math/0511511
We consider smooth 1-parameter families of plane curves tangent to a semicubic parabola, when the curvature radius of their curves at the tangency point vanishes at the cusp point. We find the \A-normal form of these families, their envelopes and local patterns near the cusp. We obtain a new codimension 2 singularity of envelopes (two transversal semicubic cusps), and we describe its perestroikas under generic small deformations.