4 citations · 14 across the 7 of their papers we have counts for
7 papers
Perestroikas of vertex sets at umbilic points
Gianmarco Capitanio, Andre Diatta
Mark all vertices on a curve evolving under a family of curves obtained by intersecting a smooth surface M with the 1-parameter family of planes parallel to the tangent plane to M…
Cusp singularities of plane envelopes
Gianmarco Capitanio
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.…
On geodesic envelopes and caustics
Gianmarco Capitanio
We give a global description of envelopes of geodesic tangents of regular curves in (not necessarily convex) Riemannian surfaces. We prove that such an envelope is the union of the…
Legendrian graphs generated by Tangential Families
Gianmarco Capitanio
We construct a Legendrian version of Envelope theory. A tangential family is a 1-parameter family of rays emanating tangentially from a smooth plane curve. The Legendrian graph of…
Simple tangential families and perestroikas of their envelopes
Gianmarco Capitanio
Tangential families are 1-parameter families of rays emanating tangentially from smooth curves. We classify tangential family germs up to Left-Right equivalence: we prove that ther…
Generic singularities of minimax solutions to Hamilton--Jacobi equations
Gianmarco Capitanio
Minimax solutions are weak solutions to Cauchy problems involving Hamilton--Jacobi equations, constructed from generating families quadratic at infinity of their geometric solution…