Matteo Raffaelli

activity

20242026

collaborators

7 papers

math.DG2026

Normal curvature of immersed tori of dimension at most $18$

Matteo Raffaelli

For $n \leq 18$ , we prove that any smooth immersion of the $n$ -torus into the closed unit ball in $R^{q}$ has a point at which the spherical average of $\lvert II(v,v)\rvert^2…

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.DG2025

A mechanical characterization of constant mean curvature surfaces

Matteo Raffaelli

The speed of a ball rolling without skidding or spinning on a surface $S$ is the length of the velocity of its center. We show that if the speed depends only on $p \in S$ , then $S$ …

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…

Normal curvature of immersed tori of dimension at most 18

h-Principles for smooth curves and knots with prescribed curvature

A mechanical characterization of constant mean curvature surfaces

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

Normal curvature of immersed tori of dimension at most $18$

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

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