Matteo Raffaelli

collaborators

4 papers

math.DG2025

$h$ -Principles for smooth curves and knots with prescribed curvature

Mohammad Ghomi, Matteo Raffaelli

We show that smooth curves with prescribed curvature satisfy a $C^{1}$ -dense $h$ -principle in the space of immersed curves in Euclidean space. More precisely, every $C^{α \geq 2}$ cur…

math.DG2024

Topology of closed asymptotic curves on negatively curved surfaces

Mohammad Ghomi, Matteo Raffaelli

Motivated by Nirenberg's problem on isometric rigidity of tight surfaces, we study closed asymptotic curves $Γ$ on negatively curved surfaces $M$ in Euclidean $3$ -space. In particu…

math.DG2024

$h$ -Principles for curves and knots of constant torsion

Mohammad Ghomi, Matteo Raffaelli

We prove that curves of constant torsion satisfy the $C^{1}$ -dense h-principle in the space of immersed curves in Euclidean space. In particular, there exists a knot of constant tors…

math.DG2024

The geometric Cauchy problem for constant-rank submanifolds

Matteo Raffaelli

Given a smooth $s$ -dimensional submanifold $S$ of $R^{m + c}$ and a smooth distribution $D \supset T S$ of rank $m$ along $S$ , we study the following geometric Cauchy problem:…

h-Principles for smooth curves and knots with prescribed curvature

Topology of closed asymptotic curves on negatively curved surfaces

h-Principles for curves and knots of constant torsion

The geometric Cauchy problem for constant-rank submanifolds

$h$ -Principles for smooth curves and knots with prescribed curvature

$h$ -Principles for curves and knots of constant torsion