Matteo Raffaelli

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20242026

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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:…

math.DG2024

Deformations of curves with constant curvature

Mohammad Ghomi, Matteo Raffaelli

We prove that curves of constant curvature satisfy the parametric $C^{1}$ -dense relative $h$ -principle in the space of immersed curves with nonvanishing curvature in Euclidean space…

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

Deformations of curves with constant curvature

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